Distributions: parameter clarification & unicode tweaks

src/Examples/ContinuousDistributions/ContinuousUniformDistribution.cs

@@ -65,7 +65,7 @@ namespace Examples.ContinuousDistributionsExamples
         {
             // 1. Initialize the new instance of the ContinuousUniform distribution class with default parameters.
             var continuousUniform = new ContinuousUniform();
-            Console.WriteLine(@"1. Initialize the new instance of the ContinuousUniform distribution class with parameters Lower = {0}, Upper = {1}", continuousUniform.Lower, continuousUniform.Upper);
+            Console.WriteLine(@"1. Initialize the new instance of the ContinuousUniform distribution class with parameters Lower = {0}, Upper = {1}", continuousUniform.LowerBound, continuousUniform.UpperBound);
             Console.WriteLine();
 
             // 2. Distributuion properties:
@@ -131,8 +131,8 @@ namespace Examples.ContinuousDistributionsExamples
 
             // 5. Generate 100000 samples of the ContinuousUniform(2, 10) distribution and display histogram
             Console.WriteLine(@"5. Generate 100000 samples of the ContinuousUniform(2, 10) distribution and display histogram");
-            continuousUniform.Upper = 10;
-            continuousUniform.Lower = 2;
+            continuousUniform.UpperBound = 10;
+            continuousUniform.LowerBound = 2;
             for (var i = 0; i < data.Length; i++)
             {
                 data[i] = continuousUniform.Sample();

src/Examples/ContinuousDistributions/ExponentialDistribution.cs

@@ -65,7 +65,7 @@ namespace Examples.ContinuousDistributionsExamples
         {
             // 1. Initialize the new instance of the Exponential distribution class with parameter Lambda = 1.
             var exponential = new Exponential(1);
-            Console.WriteLine(@"1. Initialize the new instance of the Exponential distribution class with parameter Lambda = {0}", exponential.Lambda);
+            Console.WriteLine(@"1. Initialize the new instance of the Exponential distribution class with parameter Lambda = {0}", exponential.Rate);
             Console.WriteLine();
 
             // 2. Distributuion properties:
@@ -131,7 +131,7 @@ namespace Examples.ContinuousDistributionsExamples
 
             // 5. Generate 100000 samples of the Exponential(9) distribution and display histogram
             Console.WriteLine(@"5. Generate 100000 samples of the Exponential(9) distribution and display histogram");
-            exponential.Lambda = 9;
+            exponential.Rate = 9;
             for (var i = 0; i < data.Length; i++)
             {
                 data[i] = exponential.Sample();
@@ -142,7 +142,7 @@ namespace Examples.ContinuousDistributionsExamples
 
             // 6. Generate 100000 samples of the Exponential(0.01) distribution and display histogram
             Console.WriteLine(@"6. Generate 100000 samples of the Exponential(0.01) distribution and display histogram");
-            exponential.Lambda = 0.01;
+            exponential.Rate = 0.01;
             for (var i = 0; i < data.Length; i++)
             {
                 data[i] = exponential.Sample();

src/Numerics/Distributions/Bernoulli.cs

@@ -109,21 +109,21 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
+        /// Gets or sets the probability of generating a one.
         /// </summary>
-        public System.Random RandomSource
+        public double P
         {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
+            get { return _p; }
+            set { SetParameters(value); }
         }
 
         /// <summary>
-        /// Gets or sets the probability of generating a one.
+        /// Gets or sets the random number generator which is used to draw random samples.
         /// </summary>
-        public double P
+        public System.Random RandomSource
         {
-            get { return _p; }
-            set { SetParameters(value); }
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
         }
 
         /// <summary>

src/Numerics/Distributions/Beta.cs

@@ -1,4 +1,4 @@
-// <copyright file="Beta.cs" company="Math.NET">
+// <copyright file="Beta.cs" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
@@ -61,8 +61,8 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Initializes a new instance of the Beta class.
         /// </summary>
-        /// <param name="a">The a shape parameter of the Beta distribution.</param>
-        /// <param name="b">The b shape parameter of the Beta distribution.</param>
+        /// <param name="a">The α shape parameter of the Beta distribution.</param>
+        /// <param name="b">The β shape parameter of the Beta distribution.</param>
         /// <exception cref="ArgumentOutOfRangeException">If any of the Beta parameters are negative.</exception>
         public Beta(double a, double b)
         {
@@ -73,8 +73,8 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Initializes a new instance of the Beta class.
         /// </summary>
-        /// <param name="a">The a shape parameter of the Beta distribution.</param>
-        /// <param name="b">The b shape parameter of the Beta distribution.</param>
+        /// <param name="a">The α shape parameter of the Beta distribution.</param>
+        /// <param name="b">The β shape parameter of the Beta distribution.</param>
         /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
         /// <exception cref="ArgumentOutOfRangeException">If any of the Beta parameters are negative.</exception>
         public Beta(double a, double b, System.Random randomSource)
@@ -89,14 +89,14 @@ namespace MathNet.Numerics.Distributions
         /// <returns>A string representation of the Beta distribution.</returns>
         public override string ToString()
         {
-            return "Beta(A = " + _shapeA + ", B = " + _shapeB + ")";
+            return "Beta(α = " + _shapeA + ", β = " + _shapeB + ")";
         }
 
         /// <summary>
         /// Checks whether the parameters of the distribution are valid. 
         /// </summary>
-        /// <param name="a">The a shape parameter of the Beta distribution.</param>
-        /// <param name="b">The b shape parameter of the Beta distribution.</param>
+        /// <param name="a">The α shape parameter of the Beta distribution.</param>
+        /// <param name="b">The β shape parameter of the Beta distribution.</param>
         /// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
         static bool IsValidParameterSet(double a, double b)
         {
@@ -106,8 +106,8 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Sets the parameters of the distribution after checking their validity.
         /// </summary>
-        /// <param name="a">The a shape parameter of the Beta distribution.</param>
-        /// <param name="b">The b shape parameter of the Beta distribution.</param>
+        /// <param name="a">The α shape parameter of the Beta distribution.</param>
+        /// <param name="b">The β shape parameter of the Beta distribution.</param>
         /// <exception cref="ArgumentOutOfRangeException">When the parameters don't pass the <see cref="IsValidParameterSet"/> function.</exception>
         void SetParameters(double a, double b)
         {
@@ -121,16 +121,7 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
-        /// </summary>
-        public System.Random RandomSource
-        {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
-        }
-
-        /// <summary>
-        /// Gets or sets the A shape parameter of the Beta distribution.
+        /// Gets or sets the α shape parameter of the Beta distribution.
         /// </summary>
         public double A
         {
@@ -139,7 +130,7 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets the B shape parameter of the Beta distribution.
+        /// Gets or sets the β shape parameter of the Beta distribution.
         /// </summary>
         public double B
         {
@@ -147,6 +138,15 @@ namespace MathNet.Numerics.Distributions
             set { SetParameters(_shapeA, value); }
         }
 
+        /// <summary>
+        /// Gets or sets the random number generator which is used to draw random samples.
+        /// </summary>
+        public System.Random RandomSource
+        {
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
+        }
+
         /// <summary>
         /// Gets the mean of the Beta distribution.
         /// </summary>
@@ -524,8 +524,8 @@ namespace MathNet.Numerics.Distributions
         /// Samples Beta distributed random variables by sampling two Gamma variables and normalizing.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="a">The A shape parameter.</param>
-        /// <param name="b">The B shape parameter.</param>
+        /// <param name="a">The α shape parameter of the Beta distribution.</param>
+        /// <param name="b">The β shape parameter of the Beta distribution.</param>
         /// <returns>a random number from the Beta distribution.</returns>
         internal static double SampleUnchecked(System.Random rnd, double a, double b)
         {
@@ -559,8 +559,8 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sample from the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="a">The a shape parameter of the Beta distribution.</param>
-        /// <param name="b">The b shape parameter of the Beta distribution.</param>
+        /// <param name="a">The α shape parameter of the Beta distribution.</param>
+        /// <param name="b">The β shape parameter of the Beta distribution.</param>
         /// <returns>a sample from the distribution.</returns>
         public static double Sample(System.Random rnd, double a, double b)
         {
@@ -576,8 +576,8 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sequence of samples from the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="a">The a shape parameter of the Beta distribution.</param>
-        /// <param name="b">The b shape parameter of the Beta distribution.</param>
+        /// <param name="a">The α shape parameter of the Beta distribution.</param>
+        /// <param name="b">The β shape parameter of the Beta distribution.</param>
         /// <returns>a sequence of samples from the distribution.</returns>
         public static IEnumerable<double> Samples(System.Random rnd, double a, double b)
         {

src/Numerics/Distributions/Binomial.cs

@@ -49,20 +49,13 @@ namespace MathNet.Numerics.Distributions
     {
         System.Random _random;
 
-        /// <summary>
-        /// Success probability in each trial.
-        /// </summary>
         double _p;
-
-        /// <summary>
-        /// The number of trials.
-        /// </summary>
         int _trials;
 
         /// <summary>
         /// Initializes a new instance of the Binomial class.
         /// </summary>
-        /// <param name="p">The success probability of a trial.</param>
+        /// <param name="p">The success probability in each trial.</param>
         /// <param name="n">The number of trials.</param>
         /// <exception cref="ArgumentOutOfRangeException">If <paramref name="p"/> is not in the interval [0.0,1.0].</exception>
         /// <exception cref="ArgumentOutOfRangeException">If <paramref name="n"/> is negative.</exception>
@@ -75,7 +68,7 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Initializes a new instance of the Binomial class.
         /// </summary>
-        /// <param name="p">The success probability of a trial.</param>
+        /// <param name="p">The success probability in each trial.</param>
         /// <param name="n">The number of trials.</param>
         /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
         /// <exception cref="ArgumentOutOfRangeException">If <paramref name="p"/> is not in the interval [0.0,1.0].</exception>
@@ -125,16 +118,7 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
-        /// </summary>
-        public System.Random RandomSource
-        {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
-        }
-
-        /// <summary>
-        /// Gets or sets the success probability.
+        /// Gets or sets the success probability in each trial.
         /// </summary>
         public double P
         {
@@ -151,6 +135,15 @@ namespace MathNet.Numerics.Distributions
             set { SetParameters(_p, value); }
         }
 
+        /// <summary>
+        /// Gets or sets the random number generator which is used to draw random samples.
+        /// </summary>
+        public System.Random RandomSource
+        {
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
+        }
+
         /// <summary>
         /// Gets the mean of the distribution.
         /// </summary>

src/Numerics/Distributions/Categorical.cs

@@ -192,23 +192,22 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
+        /// Gets or sets the probability mass vector (non-negative ratios) of the multinomial.
         /// </summary>
-        public System.Random RandomSource
+        /// <remarks>Sometimes the normalized probability vector cannot be represented exactly in a floating point representation.</remarks>
+        public double[] P
         {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
+            get { return (double[])_pmfNormalized.Clone(); }
+            set { SetParameters(value); }
         }
 
         /// <summary>
-        /// Gets or sets the normalized probability vector of the multinomial.
+        /// Gets or sets the random number generator which is used to draw random samples.
         /// </summary>
-        /// <remarks>Sometimes the normalized probability vector cannot be represented
-        /// exactly in a floating point representation.</remarks>
-        public double[] P
+        public System.Random RandomSource
         {
-            get { return (double[]) _pmfNormalized.Clone(); }
-            set { SetParameters(value); }
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
         }
 
         /// <summary>

src/Numerics/Distributions/Cauchy.cs

@@ -33,7 +33,7 @@ namespace MathNet.Numerics.Distributions
     /// <summary>
     /// Continuous Univariate Cauchy distribution.
     /// The Cauchy distribution is a symmetric continuous probability distribution. For details about this distribution, see 
-    /// <a href="http://en.wikipedia.org/wiki/cauchy_distribution">Wikipedia - Cauchy distribution</a>.
+    /// <a href="http://en.wikipedia.org/wiki/Cauchy_distribution">Wikipedia - Cauchy distribution</a>.
     /// </summary>
     /// <remarks><para>The distribution will use the <see cref="System.Random"/> by default. 
     /// Users can get/set the random number generator by using the <see cref="RandomSource"/> property.</para>
@@ -44,6 +44,7 @@ namespace MathNet.Numerics.Distributions
     {
         System.Random _random;
 
+        double _location;
         double _scale;
 
         /// <summary>
@@ -56,8 +57,8 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Initializes a new instance of the <see cref="Cauchy"/> class. 
         /// </summary>
-        /// <param name="location">The location parameter for the distribution.</param>
-        /// <param name="scale">The scale parameter for the distribution.</param>
+        /// <param name="location">The location (x0) of the distribution.</param>
+        /// <param name="scale">The scale (γ) of the distribution.</param>
         /// <exception cref="ArgumentException">If <paramref name="scale"/> is negative.</exception>
         public Cauchy(double location, double scale)
         {
@@ -68,8 +69,8 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Initializes a new instance of the <see cref="Cauchy"/> class. 
         /// </summary>
-        /// <param name="location">The location parameter for the distribution.</param>
-        /// <param name="scale">The scale parameter for the distribution.</param>
+        /// <param name="location">The location (x0) of the distribution.</param>
+        /// <param name="scale">The scale (γ) of the distribution.</param>
         /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
         /// <exception cref="ArgumentException">If <paramref name="scale"/> is negative.</exception>
         public Cauchy(double location, double scale, System.Random randomSource)
@@ -84,14 +85,14 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a string representation of the distribution.</returns>
         public override string ToString()
         {
-            return "Cauchy(Location = " + Median + ", Scale = " + _scale + ")";
+            return "Cauchy(x0 = " + _location + ", γ = " + _scale + ")";
         }
 
         /// <summary>
         /// Checks whether the parameters of the distribution are valid. 
         /// </summary>
-        /// <param name="location">Location parameter.</param>
-        /// <param name="scale">Scale parameter. Must be greater than 0.</param>
+        /// <param name="location">The location (x0) of the distribution.</param>
+        /// <param name="scale">The scale (γ) of the distribution. Must be greater than 0.</param>
         /// <returns>True when the parameters are valid, <c>false</c> otherwise.</returns>
         static bool IsValidParameterSet(double location, double scale)
         {
@@ -101,8 +102,8 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Sets the parameters of the distribution after checking their validity.
         /// </summary>
-        /// <param name="location">Location parameter.</param>
-        /// <param name="scale">Scale parameter. Must be greater than 0.</param>
+        /// <param name="location">The location (x0) of the distribution.</param>
+        /// <param name="scale">The scale (γ) of the distribution. Must be greater than 0.</param>
         /// <exception cref="ArgumentOutOfRangeException">When the parameters don't pass the <see cref="IsValidParameterSet"/> function.</exception>
         void SetParameters(double location, double scale)
         {
@@ -111,37 +112,36 @@ namespace MathNet.Numerics.Distributions
                 throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
             }
 
-            Median = location;
+            _location = location;
             _scale = scale;
         }
 
         /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
-        /// </summary>
-        public System.Random RandomSource
-        {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
-        }
-
-        /// <summary>
-        /// Gets or sets the location parameter of the distribution.
+        /// Gets or sets the location  (x0) of the distribution.
         /// </summary>
         public double Location
         {
-            get { return Median; }
+            get { return _location; }
             set { SetParameters(value, _scale); }
         }
 
         /// <summary>
-        /// Gets or sets the scale parameter of the distribution.
+        /// Gets or sets the scale (γ) of the distribution.
         /// </summary>
         public double Scale
         {
             get { return _scale; }
-            set { SetParameters(Median, value); }
+            set { SetParameters(_location, value); }
         }
 
+        /// <summary>
+        /// Gets or sets the random number generator which is used to draw random samples.
+        /// </summary>
+        public System.Random RandomSource
+        {
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
+        }
 
         /// <summary>
         /// Gets the mean of the distribution.
@@ -188,13 +188,16 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         public double Mode
         {
-            get { return Median; }
+            get { return _location; }
         }
 
         /// <summary>
         /// Gets the median of the distribution.
         /// </summary>
-        public double Median { get; private set; }
+        public double Median
+        {
+            get { return _location; }
+        }
 
         /// <summary>
         /// Gets the minimum of the distribution.
@@ -219,7 +222,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the density at <paramref name="x"/>.</returns>
         public double Density(double x)
         {
-            return 1.0/(Constants.Pi*_scale*(1.0 + (((x - Median)/_scale)*((x - Median)/_scale))));
+            return 1.0/(Constants.Pi*_scale*(1.0 + (((x - _location)/_scale)*((x - _location)/_scale))));
         }
 
         /// <summary>
@@ -229,7 +232,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the log density at <paramref name="x"/>.</returns>
         public double DensityLn(double x)
         {
-            return -Math.Log(Constants.Pi*_scale*(1.0 + (((x - Median)/_scale)*((x - Median)/_scale))));
+            return -Math.Log(Constants.Pi*_scale*(1.0 + (((x - _location)/_scale)*((x - _location)/_scale))));
         }
 
         /// <summary>
@@ -239,15 +242,15 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
         public double CumulativeDistribution(double x)
         {
-            return ((1.0/Constants.Pi)*Math.Atan((x - Median)/_scale)) + 0.5;
+            return ((1.0/Constants.Pi)*Math.Atan((x - _location)/_scale)) + 0.5;
         }
 
         /// <summary>
         /// Samples the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="location">The location shape parameter.</param>
-        /// <param name="scale">The scale parameter.</param>
+        /// <param name="location">The location (x0) of the distribution.</param>
+        /// <param name="scale">The scale (γ) of the distribution.</param>
         /// <returns>a random number from the distribution.</returns>
         internal static double SampleUnchecked(System.Random rnd, double location, double scale)
         {
@@ -261,7 +264,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>A random number from this distribution.</returns>
         public double Sample()
         {
-            return SampleUnchecked(RandomSource, Median, _scale);
+            return SampleUnchecked(RandomSource, _location, _scale);
         }
 
         /// <summary>
@@ -272,7 +275,7 @@ namespace MathNet.Numerics.Distributions
         {
             while (true)
             {
-                yield return SampleUnchecked(RandomSource, Median, _scale);
+                yield return SampleUnchecked(RandomSource, _location, _scale);
             }
         }
 
@@ -280,8 +283,8 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sample from the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="location">The location shape parameter.</param>
-        /// <param name="scale">The scale parameter.</param>
+        /// <param name="location">The location (x0) of the distribution.</param>
+        /// <param name="scale">The scale (γ) of the distribution.</param>
         /// <returns>a sample from the distribution.</returns>
         public static double Sample(System.Random rnd, double location, double scale)
         {
@@ -297,8 +300,8 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sequence of samples from the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="location">The location shape parameter.</param>
-        /// <param name="scale">The scale parameter.</param>
+        /// <param name="location">The location (x0) of the distribution.</param>
+        /// <param name="scale">The scale (γ) of the distribution.</param>
         /// <returns>a sequence of samples from the distribution.</returns>
         public static IEnumerable<double> Samples(System.Random rnd, double location, double scale)
         {

src/Numerics/Distributions/Chi.cs

@@ -50,10 +50,7 @@ namespace MathNet.Numerics.Distributions
     {
         System.Random _random;
 
-        /// <summary>
-        /// Keeps track of the degrees of freedom for the Chi distribution.
-        /// </summary>
-        double _dof;
+        double _freedom;
 
         /// <summary>
         /// Initializes a new instance of the <see cref="Chi"/> class. 
@@ -82,7 +79,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a string representation of the distribution.</returns>
         public override string ToString()
         {
-            return "Chi(DoF = " + _dof + ")";
+            return "Chi(DoF = " + _freedom + ")";
         }
 
         /// <summary>
@@ -107,25 +104,25 @@ namespace MathNet.Numerics.Distributions
                 throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
             }
 
-            _dof = dof;
+            _freedom = dof;
         }
 
         /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
+        /// Gets or sets the degrees of freedom of the Chi distribution.
         /// </summary>
-        public System.Random RandomSource
+        public double DegreesOfFreedom
         {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
+            get { return _freedom; }
+            set { SetParameters(value); }
         }
 
         /// <summary>
-        /// Gets or sets the degrees of freedom of the Chi distribution.
+        /// Gets or sets the random number generator which is used to draw random samples.
         /// </summary>
-        public double DegreesOfFreedom
+        public System.Random RandomSource
         {
-            get { return _dof; }
-            set { SetParameters(value); }
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
         }
 
         /// <summary>
@@ -133,7 +130,7 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         public double Mean
         {
-            get { return Constants.Sqrt2*(SpecialFunctions.Gamma((_dof + 1.0)/2.0)/SpecialFunctions.Gamma(_dof/2.0)); }
+            get { return Constants.Sqrt2*(SpecialFunctions.Gamma((_freedom + 1.0)/2.0)/SpecialFunctions.Gamma(_freedom/2.0)); }
         }
 
         /// <summary>
@@ -141,7 +138,7 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         public double Variance
         {
-            get { return _dof - (Mean*Mean); }
+            get { return _freedom - (Mean*Mean); }
         }
 
         /// <summary>
@@ -157,7 +154,7 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         public double Entropy
         {
-            get { return SpecialFunctions.GammaLn(_dof/2.0) + ((_dof - Math.Log(2) - ((_dof - 1.0)*SpecialFunctions.DiGamma(_dof/2.0)))/2.0); }
+            get { return SpecialFunctions.GammaLn(_freedom/2.0) + ((_freedom - Math.Log(2) - ((_freedom - 1.0)*SpecialFunctions.DiGamma(_freedom/2.0)))/2.0); }
         }
 
         /// <summary>
@@ -179,12 +176,12 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                if (_dof < 1)
+                if (_freedom < 1)
                 {
                     throw new NotSupportedException();
                 }
 
-                return Math.Sqrt(_dof - 1.0);
+                return Math.Sqrt(_freedom - 1.0);
             }
         }
 
@@ -219,7 +216,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the density at <paramref name="x"/>.</returns>
         public double Density(double x)
         {
-            return (Math.Pow(2.0, 1.0 - (_dof/2.0))*Math.Pow(x, _dof - 1.0)*Math.Exp(-x*x/2.0))/SpecialFunctions.Gamma(_dof/2.0);
+            return (Math.Pow(2.0, 1.0 - (_freedom/2.0))*Math.Pow(x, _freedom - 1.0)*Math.Exp(-x*x/2.0))/SpecialFunctions.Gamma(_freedom/2.0);
         }
 
         /// <summary>
@@ -229,7 +226,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the log density at <paramref name="x"/>.</returns>
         public double DensityLn(double x)
         {
-            return ((1.0 - (_dof/2.0))*Math.Log(2.0)) + ((_dof - 1.0)*Math.Log(x)) - (x*x/2.0) - SpecialFunctions.GammaLn(_dof/2.0);
+            return ((1.0 - (_freedom/2.0))*Math.Log(2.0)) + ((_freedom - 1.0)*Math.Log(x)) - (x*x/2.0) - SpecialFunctions.GammaLn(_freedom/2.0);
         }
 
         /// <summary>
@@ -239,7 +236,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
         public double CumulativeDistribution(double x)
         {
-            return SpecialFunctions.GammaLowerIncomplete(_dof/2.0, x*x/2.0)/SpecialFunctions.Gamma(_dof/2.0);
+            return SpecialFunctions.GammaLowerIncomplete(_freedom/2.0, x*x/2.0)/SpecialFunctions.Gamma(_freedom/2.0);
         }
 
         /// <summary>
@@ -265,7 +262,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a sample from the distribution.</returns>
         public double Sample()
         {
-            return SampleUnchecked(RandomSource, (int) _dof);
+            return SampleUnchecked(RandomSource, (int) _freedom);
         }
 
         /// <summary>
@@ -274,7 +271,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a sequence of samples from the distribution.</returns>
         public IEnumerable<double> Samples()
         {
-            var dof = (int) _dof;
+            var dof = (int) _freedom;
             while (true)
             {
                 yield return SampleUnchecked(RandomSource, dof);

src/Numerics/Distributions/ChiSquare.cs

@@ -48,6 +48,8 @@ namespace MathNet.Numerics.Distributions
     {
         System.Random _random;
 
+        double _freedom;
+
         /// <summary>
         /// Initializes a new instance of the <see cref="ChiSquare"/> class. 
         /// </summary>
@@ -75,7 +77,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a string representation of the distribution.</returns>
         public override string ToString()
         {
-            return "ChiSquare(DoF = " + Mean + ")";
+            return "ChiSquare(DoF = " + _freedom + ")";
         }
 
         /// <summary>
@@ -100,38 +102,41 @@ namespace MathNet.Numerics.Distributions
                 throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
             }
 
-            Mean = dof;
+            _freedom = dof;
         }
 
         /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
+        /// Gets or sets the degrees of freedom of the <c>ChiSquare</c> distribution.
         /// </summary>
-        public System.Random RandomSource
+        public double DegreesOfFreedom
         {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
+            get { return _freedom; }
+            set { SetParameters(value); }
         }
 
         /// <summary>
-        /// Gets or sets the degrees of freedom of the <c>ChiSquare</c> distribution.
+        /// Gets or sets the random number generator which is used to draw random samples.
         /// </summary>
-        public double DegreesOfFreedom
+        public System.Random RandomSource
         {
-            get { return Mean; }
-            set { SetParameters(value); }
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
         }
 
         /// <summary>
         /// Gets the mean of the distribution.
         /// </summary>
-        public double Mean { get; private set; }
+        public double Mean
+        {
+            get { return _freedom; }
+        }
 
         /// <summary>
         /// Gets the variance of the distribution.
         /// </summary>
         public double Variance
         {
-            get { return 2.0*Mean; }
+            get { return 2.0*_freedom; }
         }
 
         /// <summary>
@@ -139,7 +144,7 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         public double StdDev
         {
-            get { return Math.Sqrt(2.0*Mean); }
+            get { return Math.Sqrt(2.0 * _freedom); }
         }
 
         /// <summary>
@@ -147,7 +152,7 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         public double Entropy
         {
-            get { return (Mean/2.0) + Math.Log(2.0*SpecialFunctions.Gamma(Mean/2.0)) + ((1.0 - (Mean/2.0))*SpecialFunctions.DiGamma(Mean/2.0)); }
+            get { return (_freedom/2.0) + Math.Log(2.0*SpecialFunctions.Gamma(_freedom/2.0)) + ((1.0 - (_freedom/2.0))*SpecialFunctions.DiGamma(_freedom/2.0)); }
         }
 
         /// <summary>
@@ -155,7 +160,7 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         public double Skewness
         {
-            get { return Math.Sqrt(8.0/Mean); }
+            get { return Math.Sqrt(8.0 / _freedom); }
         }
 
         /// <summary>
@@ -163,7 +168,7 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         public double Mode
         {
-            get { return Mean - 2.0; }
+            get { return _freedom - 2.0; }
         }
 
         /// <summary>
@@ -171,7 +176,7 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         public double Median
         {
-            get { return Mean - (2.0/3.0); }
+            get { return _freedom - (2.0 / 3.0); }
         }
 
         /// <summary>
@@ -197,7 +202,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the density at <paramref name="x"/>.</returns>
         public double Density(double x)
         {
-            return (Math.Pow(x, (Mean/2.0) - 1.0)*Math.Exp(-x/2.0))/(Math.Pow(2.0, Mean/2.0)*SpecialFunctions.Gamma(Mean/2.0));
+            return (Math.Pow(x, (_freedom / 2.0) - 1.0) * Math.Exp(-x / 2.0)) / (Math.Pow(2.0, _freedom / 2.0) * SpecialFunctions.Gamma(_freedom / 2.0));
         }
 
         /// <summary>
@@ -207,7 +212,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the log density at <paramref name="x"/>.</returns>
         public double DensityLn(double x)
         {
-            return (-x/2.0) + (((Mean/2.0) - 1.0)*Math.Log(x)) - ((Mean/2.0)*Math.Log(2)) - SpecialFunctions.GammaLn(Mean/2.0);
+            return (-x / 2.0) + (((_freedom / 2.0) - 1.0) * Math.Log(x)) - ((_freedom / 2.0) * Math.Log(2)) - SpecialFunctions.GammaLn(_freedom / 2.0);
         }
 
         /// <summary>
@@ -217,7 +222,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
         public double CumulativeDistribution(double x)
         {
-            return SpecialFunctions.GammaLowerIncomplete(Mean/2.0, x/2.0)/SpecialFunctions.Gamma(Mean/2.0);
+            return SpecialFunctions.GammaLowerIncomplete(_freedom / 2.0, x / 2.0) / SpecialFunctions.Gamma(_freedom / 2.0);
         }
 
         /// <summary>
@@ -250,7 +255,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a sample from the distribution.</returns>
         public double Sample()
         {
-            return SampleUnchecked(RandomSource, Mean);
+            return SampleUnchecked(RandomSource, _freedom);
         }
 
         /// <summary>
@@ -261,7 +266,7 @@ namespace MathNet.Numerics.Distributions
         {
             while (true)
             {
-                yield return SampleUnchecked(RandomSource, Mean);
+                yield return SampleUnchecked(RandomSource, _freedom);
             }
         }
 

src/Numerics/Distributions/ContinuousUniform.cs

@@ -48,14 +48,7 @@ namespace MathNet.Numerics.Distributions
     {
         System.Random _random;
 
-        /// <summary>
-        /// The distribution's lower bound.
-        /// </summary>
         double _lower;
-
-        /// <summary>
-        /// The distribution's upper bound.
-        /// </summary>
         double _upper;
 
         /// <summary>
@@ -127,19 +120,10 @@ namespace MathNet.Numerics.Distributions
             _upper = upper;
         }
 
-        /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
-        /// </summary>
-        public System.Random RandomSource
-        {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
-        }
-
         /// <summary>
         /// Gets or sets the lower bound of the distribution.
         /// </summary>
-        public double Lower
+        public double LowerBound
         {
             get { return _lower; }
             set { SetParameters(value, _upper); }
@@ -148,12 +132,21 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Gets or sets the upper bound of the distribution.
         /// </summary>
-        public double Upper
+        public double UpperBound
         {
             get { return _upper; }
             set { SetParameters(_lower, value); }
         }
 
+        /// <summary>
+        /// Gets or sets the random number generator which is used to draw random samples.
+        /// </summary>
+        public System.Random RandomSource
+        {
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
+        }
+
         /// <summary>
         /// Gets the mean of the distribution.
         /// </summary>

src/Numerics/Distributions/ConwayMaxwellPoisson.cs

@@ -55,11 +55,8 @@ namespace MathNet.Numerics.Distributions
     {
         System.Random _random;
 
-        /// <summary>
-        /// Since many properties of the distribution can only be computed approximately, the tolerance
-        /// level specifies how much error we accept.
-        /// </summary>
-        const double Tolerance = 1e-12;
+        double _lambda;
+        double _nu;
 
         /// <summary>
         /// The mean of the distribution.
@@ -77,20 +74,16 @@ namespace MathNet.Numerics.Distributions
         double _z = double.MinValue;
 
         /// <summary>
-        /// The lambda parameter.
-        /// </summary>
-        double _lambda;
-
-        /// <summary>
-        /// The nu parameter.
+        /// Since many properties of the distribution can only be computed approximately, the tolerance
+        /// level specifies how much error we accept.
         /// </summary>
-        double _nu;
+        const double Tolerance = 1e-12;
 
         /// <summary>
         /// Initializes a new instance of the <see cref="ConwayMaxwellPoisson"/> class. 
         /// </summary>
-        /// <param name="lambda">The lambda parameter.</param>
-        /// <param name="nu">The nu parameter.</param>
+        /// <param name="lambda">The lambda (λ) parameter.</param>
+        /// <param name="nu">The nu (ν) parameter.</param>
         public ConwayMaxwellPoisson(double lambda, double nu)
         {
             _random = new System.Random();
@@ -100,8 +93,8 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Initializes a new instance of the <see cref="ConwayMaxwellPoisson"/> class. 
         /// </summary>
-        /// <param name="lambda">The lambda parameter.</param>
-        /// <param name="nu">The nu parameter.</param>
+        /// <param name="lambda">The lambda (λ) parameter.</param>
+        /// <param name="nu">The nu (ν) parameter.</param>
         /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
         public ConwayMaxwellPoisson(double lambda, double nu, System.Random randomSource)
         {
@@ -112,19 +105,17 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Returns a <see cref="System.String"/> that represents this instance.
         /// </summary>
-        /// <returns>
-        /// A <see cref="System.String"/> that represents this instance.
-        /// </returns>
+        /// <returns>A <see cref="System.String"/> that represents this instance.</returns>
         public override string ToString()
         {
-            return "ConwayMaxwellPoisson(Lambda = " + _lambda + ", Nu = " + _nu + ")";
+            return "ConwayMaxwellPoisson(λ = " + _lambda + ", ν = " + _nu + ")";
         }
 
         /// <summary>
         /// Checks whether the parameters of the distribution are valid. 
         /// </summary>
-        /// <param name="lambda">The lambda parameter.</param>
-        /// <param name="nu">The nu parameter.</param>
+        /// <param name="lambda">The lambda (λ) parameter.</param>
+        /// <param name="nu">The nu (ν) parameter.</param>
         /// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
         static bool IsValidParameterSet(double lambda, double nu)
         {
@@ -134,8 +125,8 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Sets the parameters of the distribution after checking their validity.
         /// </summary>
-        /// <param name="lambda">The lambda parameter.</param>
-        /// <param name="nu">The nu parameter.</param>
+        /// <param name="lambda">The lambda (λ) parameter.</param>
+        /// <param name="nu">The nu (ν) parameter.</param>
         /// <exception cref="ArgumentOutOfRangeException">When the parameters don't pass the <see cref="IsValidParameterSet"/> function.</exception>
         void SetParameters(double lambda, double nu)
         {
@@ -149,16 +140,7 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
-        /// </summary>
-        public System.Random RandomSource
-        {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
-        }
-
-        /// <summary>
-        /// Gets or sets the lambda parameter.
+        /// Gets or sets the lambda (λ) parameter.
         /// </summary>
         /// <value>The value of the lambda parameter.</value>
         public double Lambda
@@ -168,15 +150,24 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets the Nu parameter.
+        /// Gets or sets the DegreeOfFreedom (ν) parameter.
         /// </summary>
-        /// <value>The value of the Nu parameter.</value>
+        /// <value>The value of the DegreeOfFreedom parameter.</value>
         public double Nu
         {
             get { return _nu; }
             set { SetParameters(_lambda, value); }
         }
 
+        /// <summary>
+        /// Gets or sets the random number generator which is used to draw random samples.
+        /// </summary>
+        public System.Random RandomSource
+        {
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
+        }
+
         /// <summary>
         /// Gets the mean of the distribution.
         /// </summary>
@@ -454,8 +445,8 @@ namespace MathNet.Numerics.Distributions
         /// Returns one trials from the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="lambda">The lambda parameter</param>
-        /// <param name="nu">The nu parameter.</param>
+        /// <param name="lambda">The lambda (λ) parameter.</param>
+        /// <param name="nu">The nu (ν) parameter.</param>
         /// <param name="z">The z parameter.</param>
         /// <returns>
         /// One sample from the distribution implied by <paramref name="lambda"/>, <paramref name="nu"/>, and <paramref name="z"/>.
@@ -504,8 +495,8 @@ namespace MathNet.Numerics.Distributions
         /// Samples a random variable.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="lambda">The lambda parameter</param>
-        /// <param name="nu">The nu parameter.</param>
+        /// <param name="lambda">The lambda (λ) parameter.</param>
+        /// <param name="nu">The nu (ν) parameter.</param>
         public static int Sample(System.Random rnd, double lambda, double nu)
         {
             if (Control.CheckDistributionParameters && !IsValidParameterSet(lambda, nu))
@@ -521,8 +512,8 @@ namespace MathNet.Numerics.Distributions
         /// Samples a sequence of this random variable.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="lambda">The lambda parameter</param>
-        /// <param name="nu">The nu parameter.</param>
+        /// <param name="lambda">The lambda (λ) parameter.</param>
+        /// <param name="nu">The nu (ν) parameter.</param>
         public static IEnumerable<int> Samples(System.Random rnd, double lambda, double nu)
         {
             if (Control.CheckDistributionParameters && !IsValidParameterSet(lambda, nu))

src/Numerics/Distributions/Dirichlet.cs

@@ -47,9 +47,6 @@ namespace MathNet.Numerics.Distributions
     {
         System.Random _random;
 
-        /// <summary>
-        /// The Dirichlet distribution parameters.
-        /// </summary>
         double[] _alpha;
 
         /// <summary>
@@ -167,6 +164,15 @@ namespace MathNet.Numerics.Distributions
             _alpha = (double[]) alpha.Clone();
         }
 
+        /// <summary>
+        /// Gets or sets the parameters of the Dirichlet distribution.
+        /// </summary>
+        public double[] Alpha
+        {
+            get { return _alpha; }
+            set { SetParameters(value); }
+        }
+
         /// <summary>
         /// Gets or sets the random number generator which is used to draw random samples.
         /// </summary>
@@ -184,15 +190,6 @@ namespace MathNet.Numerics.Distributions
             get { return _alpha.Length; }
         }
 
-        /// <summary>
-        /// Gets or sets the parameters of the Dirichlet distribution.
-        /// </summary>
-        public double[] Alpha
-        {
-            get { return _alpha; }
-            set { SetParameters(value); }
-        }
-
         /// <summary>
         /// Gets the sum of the Dirichlet parameters.
         /// </summary>

src/Numerics/Distributions/DiscreteUniform.cs

@@ -49,14 +49,7 @@ namespace MathNet.Numerics.Distributions
     {
         System.Random _random;
 
-        /// <summary>
-        /// The distribution's lower bound.
-        /// </summary>
         int _lower;
-
-        /// <summary>
-        /// The distribution's upper bound.
-        /// </summary>
         int _upper;
 
         /// <summary>
@@ -121,15 +114,6 @@ namespace MathNet.Numerics.Distributions
             _upper = upper;
         }
 
-        /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
-        /// </summary>
-        public System.Random RandomSource
-        {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
-        }
-
         /// <summary>
         /// Gets or sets the lower bound of the probability distribution.
         /// </summary>
@@ -148,6 +132,15 @@ namespace MathNet.Numerics.Distributions
             set { SetParameters(_lower, value); }
         }
 
+        /// <summary>
+        /// Gets or sets the random number generator which is used to draw random samples.
+        /// </summary>
+        public System.Random RandomSource
+        {
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
+        }
+
         /// <summary>
         /// Gets the mean of the distribution.
         /// </summary>

src/Numerics/Distributions/Erlang.cs

@@ -50,37 +50,37 @@ namespace MathNet.Numerics.Distributions
         System.Random _random;
 
         double _shape;
-        double _invScale;
+        double _rate;
 
         /// <summary>
         /// Initializes a new instance of the <see cref="Erlang"/> class. 
         /// </summary>
-        /// <param name="shape">The shape of the Erlang distribution.</param>
-        /// <param name="invScale">The inverse scale of the Erlang distribution.</param>
-        public Erlang(int shape, double invScale)
+        /// <param name="shape">The shape (k) of the Erlang distribution.</param>
+        /// <param name="rate">The rate or inverse scale (λ) of the Erlang distribution.</param>
+        public Erlang(int shape, double rate)
         {
             _random = new System.Random();
-            SetParameters(shape, invScale);
+            SetParameters(shape, rate);
         }
 
         /// <summary>
         /// Initializes a new instance of the <see cref="Erlang"/> class. 
         /// </summary>
-        /// <param name="shape">The shape of the Erlang distribution.</param>
-        /// <param name="invScale">The inverse scale of the Erlang distribution.</param>
+        /// <param name="shape">The shape (k) of the Erlang distribution.</param>
+        /// <param name="rate">The rate or inverse scale (λ) of the Erlang distribution.</param>
         /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
-        public Erlang(int shape, double invScale, System.Random randomSource)
+        public Erlang(int shape, double rate, System.Random randomSource)
         {
             _random = randomSource ?? new System.Random();
-            SetParameters(shape, invScale);
+            SetParameters(shape, rate);
         }
 
         /// <summary>
         /// Constructs a Erlang distribution from a shape and scale parameter. The distribution will
         /// be initialized with the default <seealso cref="System.Random"/> random number generator.
         /// </summary>
-        /// <param name="shape">The shape of the Erlang distribution.</param>
-        /// <param name="scale">The scale of the Erlang distribution.</param>
+        /// <param name="shape">The shape (k) of the Erlang distribution.</param>
+        /// <param name="scale">The scale (mu) of the Erlang distribution.</param>
         /// <returns>a normal distribution.</returns>
         public static Erlang WithShapeScale(int shape, double scale)
         {
@@ -91,12 +91,12 @@ namespace MathNet.Numerics.Distributions
         /// Constructs a Erlang distribution from a shape and inverse scale parameter. The distribution will
         /// be initialized with the default <seealso cref="System.Random"/> random number generator.
         /// </summary>
-        /// <param name="shape">The shape of the Erlang distribution.</param>
-        /// <param name="invScale">The inverse scale of the Erlang distribution.</param>
+        /// <param name="shape">The shape (k) of the Erlang distribution.</param>
+        /// <param name="rate">The rate or inverse scale (λ) of the Erlang distribution.</param>
         /// <returns>a normal distribution.</returns>
-        public static Erlang WithShapeInvScale(int shape, double invScale)
+        public static Erlang WithShapeRate(int shape, double rate)
         {
-            return new Erlang(shape, invScale);
+            return new Erlang(shape, rate);
         }
 
         /// <summary>
@@ -105,52 +105,52 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a string representation of the distribution.</returns>
         public override string ToString()
         {
-            return "Erlang(Shape = " + _shape + ", Inverse Scale = " + _invScale + ")";
+            return "Erlang(Shape = " + _shape + ", λ = " + _rate + ")";
         }
 
         /// <summary>
         /// Checks whether the parameters of the distribution are valid.
         /// </summary>
-        /// <param name="shape">The shape of the Erlang distribution.</param>
-        /// <param name="invScale">The inverse scale of the Erlang distribution.</param>
+        /// <param name="shape">The shape (k) of the Erlang distribution.</param>
+        /// <param name="rate">The rate or inverse scale (λ) of the Erlang distribution.</param>
         /// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
-        static bool IsValidParameterSet(double shape, double invScale)
+        static bool IsValidParameterSet(double shape, double rate)
         {
-            return shape >= 0.0 && invScale >= 0.0;
+            return shape >= 0.0 && rate >= 0.0;
         }
 
         /// <summary>
         /// Sets the parameters of the distribution after checking their validity.
         /// </summary>
-        /// <param name="shape">The shape of the Erlang distribution.</param>
-        /// <param name="invScale">The inverse scale of the Erlang distribution.</param>
-        void SetParameters(double shape, double invScale)
+        /// <param name="shape">The shape (k) of the Erlang distribution.</param>
+        /// <param name="rate">The rate or inverse scale (λ) of the Erlang distribution.</param>
+        void SetParameters(double shape, double rate)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(shape, invScale))
+            if (Control.CheckDistributionParameters && !IsValidParameterSet(shape, rate))
             {
                 throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
             }
 
             _shape = shape;
-            _invScale = invScale;
+            _rate = rate;
         }
 
         /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
+        /// Gets or sets the shape (k) of the Erlang distribution.
         /// </summary>
-        public System.Random RandomSource
+        public int Shape
         {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
+            get { return (int)_shape; }
+            set { SetParameters(value, _rate); }
         }
 
         /// <summary>
-        /// Gets or sets the shape of the Erlang distribution.
+        /// Gets or sets the rate or inverse scale (λ) of the Erlang distribution.
         /// </summary>
-        public int Shape
+        public double Rate
         {
-            get { return (int) _shape; }
-            set { SetParameters(value, _invScale); }
+            get { return _rate; }
+            set { SetParameters(_shape, value); }
         }
 
         /// <summary>
@@ -158,27 +158,25 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         public double Scale
         {
-            get { return 1.0/_invScale; }
+            get { return 1.0 / _rate; }
             set
             {
-                var invScale = 1.0/value;
-
+                var invScale = 1.0 / value;
                 if (Double.IsNegativeInfinity(invScale))
                 {
                     invScale = -invScale;
                 }
-
                 SetParameters(_shape, invScale);
             }
         }
 
         /// <summary>
-        /// Gets or sets the inverse scale of the Erlang distribution.
+        /// Gets or sets the random number generator which is used to draw random samples.
         /// </summary>
-        public double InvScale
+        public System.Random RandomSource
         {
-            get { return _invScale; }
-            set { SetParameters(_shape, value); }
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
         }
 
         /// <summary>
@@ -188,17 +186,17 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                if (Double.IsPositiveInfinity(_invScale))
+                if (Double.IsPositiveInfinity(_rate))
                 {
                     return _shape;
                 }
 
-                if (_invScale == 0.0 && _shape == 0.0)
+                if (_rate == 0.0 && _shape == 0.0)
                 {
                     return Double.NaN;
                 }
 
-                return _shape/_invScale;
+                return _shape/_rate;
             }
         }
 
@@ -209,17 +207,17 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                if (Double.IsPositiveInfinity(_invScale))
+                if (Double.IsPositiveInfinity(_rate))
                 {
                     return 0.0;
                 }
 
-                if (_invScale == 0.0 && _shape == 0.0)
+                if (_rate == 0.0 && _shape == 0.0)
                 {
                     return Double.NaN;
                 }
 
-                return _shape/(_invScale*_invScale);
+                return _shape/(_rate*_rate);
             }
         }
 
@@ -230,17 +228,17 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                if (Double.IsPositiveInfinity(_invScale))
+                if (Double.IsPositiveInfinity(_rate))
                 {
                     return 0.0;
                 }
 
-                if (_invScale == 0.0 && _shape == 0.0)
+                if (_rate == 0.0 && _shape == 0.0)
                 {
                     return Double.NaN;
                 }
 
-                return Math.Sqrt(_shape)/_invScale;
+                return Math.Sqrt(_shape)/_rate;
             }
         }
 
@@ -251,17 +249,17 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                if (Double.IsPositiveInfinity(_invScale))
+                if (Double.IsPositiveInfinity(_rate))
                 {
                     return 0.0;
                 }
 
-                if (_invScale == 0.0 && _shape == 0.0)
+                if (_rate == 0.0 && _shape == 0.0)
                 {
                     return Double.NaN;
                 }
 
-                return _shape - Math.Log(_invScale) + SpecialFunctions.GammaLn(_shape) + ((1.0 - _shape)*SpecialFunctions.DiGamma(_shape));
+                return _shape - Math.Log(_rate) + SpecialFunctions.GammaLn(_shape) + ((1.0 - _shape)*SpecialFunctions.DiGamma(_shape));
             }
         }
 
@@ -272,12 +270,12 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                if (Double.IsPositiveInfinity(_invScale))
+                if (Double.IsPositiveInfinity(_rate))
                 {
                     return 0.0;
                 }
 
-                if (_invScale == 0.0 && _shape == 0.0)
+                if (_rate == 0.0 && _shape == 0.0)
                 {
                     return Double.NaN;
                 }
@@ -298,17 +296,17 @@ namespace MathNet.Numerics.Distributions
                     throw new NotSupportedException();
                 }
 
-                if (Double.IsPositiveInfinity(_invScale))
+                if (Double.IsPositiveInfinity(_rate))
                 {
                     return _shape;
                 }
 
-                if (_invScale == 0.0 && _shape == 0.0)
+                if (_rate == 0.0 && _shape == 0.0)
                 {
                     return Double.NaN;
                 }
 
-                return (_shape - 1.0)/_invScale;
+                return (_shape - 1.0)/_rate;
             }
         }
 
@@ -343,22 +341,22 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the density at <paramref name="x"/>.</returns>
         public double Density(double x)
         {
-            if (Double.IsPositiveInfinity(_invScale))
+            if (Double.IsPositiveInfinity(_rate))
             {
                 return x == _shape ? Double.PositiveInfinity : 0.0;
             }
 
-            if (_shape == 0.0 && _invScale == 0.0)
+            if (_shape == 0.0 && _rate == 0.0)
             {
                 return 0.0;
             }
 
             if (_shape == 1.0)
             {
-                return _invScale*Math.Exp(-_invScale*x);
+                return _rate*Math.Exp(-_rate*x);
             }
 
-            return Math.Pow(_invScale, _shape)*Math.Pow(x, _shape - 1.0)*Math.Exp(-_invScale*x)/SpecialFunctions.Gamma(_shape);
+            return Math.Pow(_rate, _shape)*Math.Pow(x, _shape - 1.0)*Math.Exp(-_rate*x)/SpecialFunctions.Gamma(_shape);
         }
 
         /// <summary>
@@ -368,22 +366,22 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the log density at <paramref name="x"/>.</returns>
         public double DensityLn(double x)
         {
-            if (Double.IsPositiveInfinity(_invScale))
+            if (Double.IsPositiveInfinity(_rate))
             {
                 return x == _shape ? Double.PositiveInfinity : Double.NegativeInfinity;
             }
 
-            if (_shape == 0.0 && _invScale == 0.0)
+            if (_shape == 0.0 && _rate == 0.0)
             {
                 return Double.NegativeInfinity;
             }
 
             if (_shape == 1.0)
             {
-                return Math.Log(_invScale) - (_invScale*x);
+                return Math.Log(_rate) - (_rate*x);
             }
 
-            return (_shape*Math.Log(_invScale)) + ((_shape - 1.0)*Math.Log(x)) - (_invScale*x) - SpecialFunctions.GammaLn(_shape);
+            return (_shape*Math.Log(_rate)) + ((_shape - 1.0)*Math.Log(x)) - (_rate*x) - SpecialFunctions.GammaLn(_shape);
         }
 
         /// <summary>
@@ -393,17 +391,17 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
         public double CumulativeDistribution(double x)
         {
-            if (Double.IsPositiveInfinity(_invScale))
+            if (Double.IsPositiveInfinity(_rate))
             {
                 return x >= _shape ? 1.0 : 0.0;
             }
 
-            if (_shape == 0.0 && _invScale == 0.0)
+            if (_shape == 0.0 && _rate == 0.0)
             {
                 return 0.0;
             }
 
-            return SpecialFunctions.GammaLowerRegularized(_shape, x*_invScale);
+            return SpecialFunctions.GammaLowerRegularized(_shape, x*_rate);
         }
 
         /// <summary>
@@ -466,7 +464,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a sample from the distribution.</returns>
         public double Sample()
         {
-            return SampleUnchecked(RandomSource, _shape, _invScale);
+            return SampleUnchecked(RandomSource, _shape, _rate);
         }
 
         /// <summary>
@@ -477,7 +475,7 @@ namespace MathNet.Numerics.Distributions
         {
             while (true)
             {
-                yield return SampleUnchecked(RandomSource, _shape, _invScale);
+                yield return SampleUnchecked(RandomSource, _shape, _rate);
             }
         }
 

src/Numerics/Distributions/Exponential.cs

@@ -37,7 +37,7 @@ namespace MathNet.Numerics.Distributions
     /// <summary>
     /// Continuous Univariate Exponential distribution.
     /// The exponential distribution is a distribution over the real numbers parameterized by one non-negative parameter.
-    /// <a href="http://en.wikipedia.org/wiki/exponential_distribution">Wikipedia - exponential distribution</a>.
+    /// <a href="http://en.wikipedia.org/wiki/Exponential_distribution">Wikipedia - exponential distribution</a>.
     /// </summary>
     /// <remarks>The distribution will use the <see cref="System.Random"/> by default. 
     /// <para>Users can set the random number generator by using the <see cref="RandomSource"/> property.</para>
@@ -48,27 +48,27 @@ namespace MathNet.Numerics.Distributions
     {
         System.Random _random;
 
-        double _lambda;
+        double _rate;
 
         /// <summary>
         /// Initializes a new instance of the <see cref="Exponential"/> class.
         /// </summary>
-        /// <param name="lambda">The lambda parameter of the Exponential distribution.</param>
-        public Exponential(double lambda)
+        /// <param name="rate">The rate (λ) parameter of the Exponential distribution.</param>
+        public Exponential(double rate)
         {
             _random = new System.Random();
-            SetParameters(lambda);
+            SetParameters(rate);
         }
 
         /// <summary>
         /// Initializes a new instance of the <see cref="Exponential"/> class.
         /// </summary>
-        /// <param name="lambda">The lambda parameter of the Exponential distribution.</param>
+        /// <param name="rate">The rate (λ) parameter of the Exponential distribution.</param>
         /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
-        public Exponential(double lambda, System.Random randomSource)
+        public Exponential(double rate, System.Random randomSource)
         {
             _random = randomSource ?? new System.Random();
-            SetParameters(lambda);
+            SetParameters(rate);
         }
 
         /// <summary>
@@ -77,50 +77,50 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a string representation of the distribution.</returns>
         public override string ToString()
         {
-            return "Exponential(Lambda = " + _lambda + ")";
+            return "Exponential(λ = " + _rate + ")";
         }
 
         /// <summary>
         /// Checks whether the parameters of the distribution are valid. 
         /// </summary>
-        /// <param name="lambda">Lambda parameter.</param>
+        /// <param name="rate">The rate (λ) parameter of the Exponential distribution.</param>
         /// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
-        static bool IsValidParameterSet(double lambda)
+        static bool IsValidParameterSet(double rate)
         {
-            return lambda >= 0.0;
+            return rate >= 0.0;
         }
 
         /// <summary>
         /// Sets the parameters of the distribution after checking their validity.
         /// </summary>
-        /// <param name="lambda">Lambda parameter.</param>
+        /// <param name="rate">The rate (λ) parameter of the Exponential distribution.</param>
         /// <exception cref="ArgumentOutOfRangeException">When the parameters don't pass the <see cref="IsValidParameterSet"/> function.</exception>
-        void SetParameters(double lambda)
+        void SetParameters(double rate)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(lambda))
+            if (Control.CheckDistributionParameters && !IsValidParameterSet(rate))
             {
                 throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
             }
 
-            _lambda = lambda;
+            _rate = rate;
         }
 
         /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
+        /// Gets or sets the rate (λ) parameter of the distribution.
         /// </summary>
-        public System.Random RandomSource
+        public double Rate
         {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
+            get { return _rate; }
+            set { SetParameters(value); }
         }
 
         /// <summary>
-        /// Gets or sets the lambda parameter of the distribution.
+        /// Gets or sets the random number generator which is used to draw random samples.
         /// </summary>
-        public double Lambda
+        public System.Random RandomSource
         {
-            get { return _lambda; }
-            set { SetParameters(value); }
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
         }
 
         /// <summary>
@@ -128,7 +128,7 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         public double Mean
         {
-            get { return 1.0/_lambda; }
+            get { return 1.0/_rate; }
         }
 
         /// <summary>
@@ -136,7 +136,7 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         public double Variance
         {
-            get { return 1.0/(_lambda*_lambda); }
+            get { return 1.0/(_rate*_rate); }
         }
 
         /// <summary>
@@ -144,7 +144,7 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         public double StdDev
         {
-            get { return 1.0/_lambda; }
+            get { return 1.0/_rate; }
         }
 
         /// <summary>
@@ -152,7 +152,7 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         public double Entropy
         {
-            get { return 1.0 - Math.Log(_lambda); }
+            get { return 1.0 - Math.Log(_rate); }
         }
 
         /// <summary>
@@ -176,7 +176,7 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         public double Median
         {
-            get { return Math.Log(2.0)/_lambda; }
+            get { return Math.Log(2.0)/_rate; }
         }
 
         /// <summary>
@@ -204,7 +204,7 @@ namespace MathNet.Numerics.Distributions
         {
             if (x >= 0.0)
             {
-                return _lambda*Math.Exp(-_lambda*x);
+                return _rate*Math.Exp(-_rate*x);
             }
 
             return 0.0;
@@ -217,7 +217,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the log density at <paramref name="x"/>.</returns>
         public double DensityLn(double x)
         {
-            return Math.Log(_lambda) - (_lambda*x);
+            return Math.Log(_rate) - (_rate*x);
         }
 
         /// <summary>
@@ -229,7 +229,7 @@ namespace MathNet.Numerics.Distributions
         {
             if (x >= 0.0)
             {
-                return 1.0 - Math.Exp(-_lambda*x);
+                return 1.0 - Math.Exp(-_rate*x);
             }
 
             return 0.0;
@@ -239,9 +239,9 @@ namespace MathNet.Numerics.Distributions
         /// Samples the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="lambda">The lambda parameter of the Exponential distribution.</param>
+        /// <param name="rate">The rate (λ) parameter of the Exponential distribution.</param>
         /// <returns>a random number from the distribution.</returns>
-        internal static double SampleUnchecked(System.Random rnd, double lambda)
+        internal static double SampleUnchecked(System.Random rnd, double rate)
         {
             var r = rnd.NextDouble();
             while (r == 0.0)
@@ -249,7 +249,7 @@ namespace MathNet.Numerics.Distributions
                 r = rnd.NextDouble();
             }
 
-            return -Math.Log(r)/lambda;
+            return -Math.Log(r)/rate;
         }
 
         /// <summary>
@@ -258,7 +258,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>A random number from this distribution.</returns>
         public double Sample()
         {
-            return SampleUnchecked(RandomSource, _lambda);
+            return SampleUnchecked(RandomSource, _rate);
         }
 
         /// <summary>
@@ -269,7 +269,7 @@ namespace MathNet.Numerics.Distributions
         {
             while (true)
             {
-                yield return SampleUnchecked(RandomSource, _lambda);
+                yield return SampleUnchecked(RandomSource, _rate);
             }
         }
 
@@ -277,34 +277,34 @@ namespace MathNet.Numerics.Distributions
         /// Draws a random sample from the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="lambda">The lambda parameter of the Exponential distribution.</param>
+        /// <param name="rate">The rate (λ) parameter of the Exponential distribution.</param>
         /// <returns>A random number from this distribution.</returns>
-        public static double Sample(System.Random rnd, double lambda)
+        public static double Sample(System.Random rnd, double rate)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(lambda))
+            if (Control.CheckDistributionParameters && !IsValidParameterSet(rate))
             {
                 throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
             }
 
-            return SampleUnchecked(rnd, lambda);
+            return SampleUnchecked(rnd, rate);
         }
 
         /// <summary>
         /// Generates a sequence of samples from the Exponential distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="lambda">The lambda parameter of the Exponential distribution.</param>
+        /// <param name="rate">The rate (λ) parameter of the Exponential distribution.</param>
         /// <returns>a sequence of samples from the distribution.</returns>
-        public static IEnumerable<double> Samples(System.Random rnd, double lambda)
+        public static IEnumerable<double> Samples(System.Random rnd, double rate)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(lambda))
+            if (Control.CheckDistributionParameters && !IsValidParameterSet(rate))
             {
                 throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
             }
 
             while (true)
             {
-                yield return SampleUnchecked(rnd, lambda);
+                yield return SampleUnchecked(rnd, rate);
             }
         }
     }

src/Numerics/Distributions/FisherSnedecor.cs

@@ -48,15 +48,8 @@ namespace MathNet.Numerics.Distributions
     {
         System.Random _random;
 
-        /// <summary>
-        /// The first parameter - degree of freedom.
-        /// </summary>
-        double _d1;
-
-        /// <summary>
-        /// The second parameter - degree of freedom.
-        /// </summary>
-        double _d2;
+        double _freedom1;
+        double _freedom2;
 
         /// <summary>
         /// Initializes a new instance of the <see cref="FisherSnedecor"/> class. 
@@ -87,7 +80,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a string representation of the distribution.</returns>
         public override string ToString()
         {
-            return "FisherSnedecor(DegreeOfFreedom1 = " + _d1 + ", DegreeOfFreedom2 = " + _d2 + ")";
+            return "FisherSnedecor(DegreeOfFreedom1 = " + _freedom1 + ", DegreeOfFreedom2 = " + _freedom2 + ")";
         }
 
         /// <summary>
@@ -113,35 +106,35 @@ namespace MathNet.Numerics.Distributions
                 throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
             }
 
-            _d1 = d1;
-            _d2 = d2;
+            _freedom1 = d1;
+            _freedom2 = d2;
         }
 
         /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
+        /// Gets or sets the first parameter - degree of freedom.
         /// </summary>
-        public System.Random RandomSource
+        public double DegreeOfFreedom1
         {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
+            get { return _freedom1; }
+            set { SetParameters(value, _freedom2); }
         }
 
         /// <summary>
-        /// Gets or sets the first parameter - degree of freedom.
+        /// Gets or sets the second parameter - degree of freedom.
         /// </summary>
-        public double DegreeOfFreedom1
+        public double DegreeOfFreedom2
         {
-            get { return _d1; }
-            set { SetParameters(value, _d2); }
+            get { return _freedom2; }
+            set { SetParameters(_freedom1, value); }
         }
 
         /// <summary>
-        /// Gets or sets the second parameter - degree of freedom.
+        /// Gets or sets the random number generator which is used to draw random samples.
         /// </summary>
-        public double DegreeOfFreedom2
+        public System.Random RandomSource
         {
-            get { return _d2; }
-            set { SetParameters(_d1, value); }
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
         }
 
         /// <summary>
@@ -151,12 +144,12 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                if (_d2 <= 2)
+                if (_freedom2 <= 2)
                 {
                     throw new NotSupportedException();
                 }
 
-                return _d2/(_d2 - 2.0);
+                return _freedom2/(_freedom2 - 2.0);
             }
         }
 
@@ -167,12 +160,12 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                if (_d2 <= 4)
+                if (_freedom2 <= 4)
                 {
                     throw new NotSupportedException();
                 }
 
-                return (2.0*_d2*_d2*(_d1 + _d2 - 2.0))/(_d1*(_d2 - 2.0)*(_d2 - 2.0)*(_d2 - 4.0));
+                return (2.0*_freedom2*_freedom2*(_freedom1 + _freedom2 - 2.0))/(_freedom1*(_freedom2 - 2.0)*(_freedom2 - 2.0)*(_freedom2 - 4.0));
             }
         }
 
@@ -199,12 +192,12 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                if (_d2 <= 6)
+                if (_freedom2 <= 6)
                 {
                     throw new NotSupportedException();
                 }
 
-                return (((2.0*_d1) + _d2 - 2.0)*Math.Sqrt(8.0*(_d2 - 4.0)))/((_d2 - 6.0)*Math.Sqrt(_d1*(_d1 + _d2 - 2.0)));
+                return (((2.0*_freedom1) + _freedom2 - 2.0)*Math.Sqrt(8.0*(_freedom2 - 4.0)))/((_freedom2 - 6.0)*Math.Sqrt(_freedom1*(_freedom1 + _freedom2 - 2.0)));
             }
         }
 
@@ -215,12 +208,12 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                if (_d1 <= 2)
+                if (_freedom1 <= 2)
                 {
                     throw new NotSupportedException();
                 }
 
-                return (_d2*(_d1 - 2.0))/(_d1*(_d2 + 2.0));
+                return (_freedom2*(_freedom1 - 2.0))/(_freedom1*(_freedom2 + 2.0));
             }
         }
 
@@ -255,7 +248,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the density at <paramref name="x"/>.</returns>
         public double Density(double x)
         {
-            return Math.Sqrt(Math.Pow(_d1*x, _d1)*Math.Pow(_d2, _d2)/Math.Pow((_d1*x) + _d2, _d1 + _d2))/(x*SpecialFunctions.Beta(_d1/2.0, _d2/2.0));
+            return Math.Sqrt(Math.Pow(_freedom1*x, _freedom1)*Math.Pow(_freedom2, _freedom2)/Math.Pow((_freedom1*x) + _freedom2, _freedom1 + _freedom2))/(x*SpecialFunctions.Beta(_freedom1/2.0, _freedom2/2.0));
         }
 
         /// <summary>
@@ -275,7 +268,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
         public double CumulativeDistribution(double x)
         {
-            return SpecialFunctions.BetaRegularized(_d1/2.0, _d2/2.0, _d1*x/((_d1*x) + _d2));
+            return SpecialFunctions.BetaRegularized(_freedom1/2.0, _freedom2/2.0, _freedom1*x/((_freedom1*x) + _freedom2));
         }
 
         /// <summary>
@@ -296,7 +289,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a sample from the distribution.</returns>
         public double Sample()
         {
-            return SampleUnchecked(RandomSource, _d1, _d2);
+            return SampleUnchecked(RandomSource, _freedom1, _freedom2);
         }
 
         /// <summary>
@@ -307,7 +300,7 @@ namespace MathNet.Numerics.Distributions
         {
             while (true)
             {
-                yield return SampleUnchecked(RandomSource, _d1, _d2);
+                yield return SampleUnchecked(RandomSource, _freedom1, _freedom2);
             }
         }
 

src/Numerics/Distributions/Gamma.cs

@@ -1,4 +1,4 @@
-// <copyright file="Gamma.cs" company="Math.NET">
+// <copyright file="Gamma.cs" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
@@ -46,7 +46,7 @@ namespace MathNet.Numerics.Distributions
     /// with shape and inverse scale both zero is undefined.</para>
     /// <para> Random number generation for the Gamma distribution is based on the algorithm in:
     /// "A Simple Method for Generating Gamma Variables" - Marsaglia &amp; Tsang
-    /// ACM Transactions on Mathematical Software, Vol. 26, No. 3, September 2000, Pages 363–372.</para>
+    /// ACM Transactions on Mathematical Software, Vol. 26, No. 3, September 2000, Pages 363–372.</para>
     /// <para>The distribution will use the <see cref="System.Random"/> by default. 
     /// Users can get/set the random number generator by using the <see cref="RandomSource"/> property.</para>
     /// <para>The statistics classes will check all the incoming parameters whether they are in the allowed
@@ -57,38 +57,37 @@ namespace MathNet.Numerics.Distributions
         System.Random _random;
 
         double _shape;
-        double _invScale;
+        double _rate;
 
         /// <summary>
         /// Initializes a new instance of the Gamma class.
         /// </summary>
-        /// <param name="shape">The shape of the Gamma distribution.</param>
-        /// <param name="invScale">The inverse scale of the Gamma distribution.</param>
-        public Gamma(double shape, double invScale)
+        /// <param name="shape">The shape (k, α) of the Gamma distribution.</param>
+        /// <param name="rate">The rate or inverse scale (β) of the Gamma distribution.</param>
+        public Gamma(double shape, double rate)
         {
             _random = new System.Random();
-            SetParameters(shape, invScale);
+            SetParameters(shape, rate);
         }
 
         /// <summary>
         /// Initializes a new instance of the Gamma class.
         /// </summary>
-        /// <param name="shape">The shape of the Gamma distribution.</param>
-        /// <param name="invScale">The inverse scale of the Gamma distribution.</param>
+        /// <param name="shape">The shape (k, α) of the Gamma distribution.</param>
+        /// <param name="rate">The rate or inverse scale (β) of the Gamma distribution.</param>
         /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
-        public Gamma(double shape, double invScale, System.Random randomSource)
+        public Gamma(double shape, double rate, System.Random randomSource)
         {
             _random = randomSource ?? new System.Random();
-            SetParameters(shape, invScale);
+            SetParameters(shape, rate);
         }
 
         /// <summary>
         /// Constructs a Gamma distribution from a shape and scale parameter. The distribution will
         /// be initialized with the default <seealso cref="System.Random"/> random number generator.
         /// </summary>
-        /// <param name="shape">The shape of the Gamma distribution.</param>
-        /// <param name="scale">The scale of the Gamma distribution.</param>
-        /// <returns>a normal distribution.</returns>
+        /// <param name="shape">The shape (k) of the Gamma distribution.</param>
+        /// <param name="scale">The scale (θ) of the Gamma distribution.</param>
         public static Gamma WithShapeScale(double shape, double scale)
         {
             return new Gamma(shape, 1.0/scale);
@@ -98,12 +97,11 @@ namespace MathNet.Numerics.Distributions
         /// Constructs a Gamma distribution from a shape and inverse scale parameter. The distribution will
         /// be initialized with the default <seealso cref="System.Random"/> random number generator.
         /// </summary>
-        /// <param name="shape">The shape of the Gamma distribution.</param>
-        /// <param name="invScale">The inverse scale of the Gamma distribution.</param>
-        /// <returns>a normal distribution.</returns>
-        public static Gamma WithShapeInvScale(double shape, double invScale)
+        /// <param name="shape">The shape (α) of the Gamma distribution.</param>
+        /// <param name="rate">The rate or inverse scale (β) of the Gamma distribution.</param>
+        public static Gamma WithShapeRate(double shape, double rate)
         {
-            return new Gamma(shape, invScale);
+            return new Gamma(shape, rate);
         }
 
         /// <summary>
@@ -112,81 +110,79 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a string representation of the distribution.</returns>
         public override string ToString()
         {
-            return "Gamma(Shape = " + _shape + ", Inverse Scale = " + _invScale + ")";
+            return "Gamma(α = " + _shape + ", β = " + _rate + ")";
         }
 
         /// <summary>
         /// Checks whether the parameters of the distribution are valid. 
         /// </summary>
-        /// <param name="shape">The shape of the Gamma distribution.</param>
-        /// <param name="invScale">The inverse scale of the Gamma distribution.</param>
+        /// <param name="shape">The shape (k, α) of the Gamma distribution.</param>
+        /// <param name="rate">The rate or inverse scale (β) of the Gamma distribution.</param>
         /// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
-        static bool IsValidParameterSet(double shape, double invScale)
+        static bool IsValidParameterSet(double shape, double rate)
         {
-            return shape >= 0.0 && invScale >= 0.0;
+            return shape >= 0.0 && rate >= 0.0;
         }
 
         /// <summary>
         /// Sets the parameters of the distribution after checking their validity.
         /// </summary>
-        /// <param name="shape">The shape of the Gamma distribution.</param>
-        /// <param name="invScale">The inverse scale of the Gamma distribution.</param>
+        /// <param name="shape">The shape (k, α) of the Gamma distribution.</param>
+        /// <param name="rate">The rate or inverse scale (β) of the Gamma distribution.</param>
         /// <exception cref="ArgumentOutOfRangeException">When the parameters don't pass the <see cref="IsValidParameterSet"/> function.</exception>
-        void SetParameters(double shape, double invScale)
+        void SetParameters(double shape, double rate)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(shape, invScale))
+            if (Control.CheckDistributionParameters && !IsValidParameterSet(shape, rate))
             {
                 throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
             }
 
             _shape = shape;
-            _invScale = invScale;
+            _rate = rate;
         }
 
         /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
+        /// Gets or sets the shape (k, α) of the Gamma distribution.
         /// </summary>
-        public System.Random RandomSource
+        public double Shape
         {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
+            get { return _shape; }
+            set { SetParameters(value, _rate); }
         }
 
         /// <summary>
-        /// Gets or sets the shape of the Gamma distribution.
+        /// Gets or sets the rate or inverse scale (β) of the Gamma distribution.
         /// </summary>
-        public double Shape
+        public double Rate
         {
-            get { return _shape; }
-            set { SetParameters(value, _invScale); }
+            get { return _rate; }
+            set { SetParameters(_shape, value); }
         }
 
         /// <summary>
-        /// Gets or sets the scale of the Gamma distribution.
+        /// Gets or sets the scale (θ) of the Gamma distribution.
         /// </summary>
         public double Scale
         {
-            get { return 1.0/_invScale; }
+            get { return 1.0 / _rate; }
             set
             {
-                var invScale = 1.0/value;
-
-                if (Double.IsNegativeInfinity(invScale))
+                var rate = 1.0 / value;
+                if (Double.IsNegativeInfinity(rate))
                 {
-                    invScale = -invScale;
+                    rate = -rate;
                 }
-
-                SetParameters(_shape, invScale);
+                SetParameters(_shape, rate);
             }
         }
 
         /// <summary>
-        /// Gets or sets the inverse scale of the Gamma distribution.
+        /// Gets or sets the random number generator which is used to draw random samples.
         /// </summary>
-        public double InvScale
+        public System.Random RandomSource
         {
-            get { return _invScale; }
-            set { SetParameters(_shape, value); }
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
         }
 
         /// <summary>
@@ -196,17 +192,17 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                if (Double.IsPositiveInfinity(_invScale))
+                if (Double.IsPositiveInfinity(_rate))
                 {
                     return _shape;
                 }
 
-                if (_invScale == 0.0 && _shape == 0.0)
+                if (_rate == 0.0 && _shape == 0.0)
                 {
                     return Double.NaN;
                 }
 
-                return _shape/_invScale;
+                return _shape/_rate;
             }
         }
 
@@ -217,17 +213,17 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                if (Double.IsPositiveInfinity(_invScale))
+                if (Double.IsPositiveInfinity(_rate))
                 {
                     return 0.0;
                 }
 
-                if (_invScale == 0.0 && _shape == 0.0)
+                if (_rate == 0.0 && _shape == 0.0)
                 {
                     return Double.NaN;
                 }
 
-                return _shape/(_invScale*_invScale);
+                return _shape/(_rate*_rate);
             }
         }
 
@@ -238,17 +234,17 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                if (Double.IsPositiveInfinity(_invScale))
+                if (Double.IsPositiveInfinity(_rate))
                 {
                     return 0.0;
                 }
 
-                if (_invScale == 0.0 && _shape == 0.0)
+                if (_rate == 0.0 && _shape == 0.0)
                 {
                     return Double.NaN;
                 }
 
-                return Math.Sqrt(_shape/(_invScale*_invScale));
+                return Math.Sqrt(_shape/(_rate*_rate));
             }
         }
 
@@ -259,17 +255,17 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                if (Double.IsPositiveInfinity(_invScale))
+                if (Double.IsPositiveInfinity(_rate))
                 {
                     return 0.0;
                 }
 
-                if (_invScale == 0.0 && _shape == 0.0)
+                if (_rate == 0.0 && _shape == 0.0)
                 {
                     return Double.NaN;
                 }
 
-                return _shape - Math.Log(_invScale) + SpecialFunctions.GammaLn(_shape) + ((1.0 - _shape)*SpecialFunctions.DiGamma(_shape));
+                return _shape - Math.Log(_rate) + SpecialFunctions.GammaLn(_shape) + ((1.0 - _shape)*SpecialFunctions.DiGamma(_shape));
             }
         }
 
@@ -280,12 +276,12 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                if (Double.IsPositiveInfinity(_invScale))
+                if (Double.IsPositiveInfinity(_rate))
                 {
                     return 0.0;
                 }
 
-                if (_invScale == 0.0 && _shape == 0.0)
+                if (_rate == 0.0 && _shape == 0.0)
                 {
                     return Double.NaN;
                 }
@@ -301,17 +297,17 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                if (Double.IsPositiveInfinity(_invScale))
+                if (Double.IsPositiveInfinity(_rate))
                 {
                     return _shape;
                 }
 
-                if (_invScale == 0.0 && _shape == 0.0)
+                if (_rate == 0.0 && _shape == 0.0)
                 {
                     return Double.NaN;
                 }
 
-                return (_shape - 1.0)/_invScale;
+                return (_shape - 1.0)/_rate;
             }
         }
 
@@ -346,22 +342,22 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the density at <paramref name="x"/>.</returns>
         public double Density(double x)
         {
-            if (Double.IsPositiveInfinity(_invScale))
+            if (Double.IsPositiveInfinity(_rate))
             {
                 return x == _shape ? Double.PositiveInfinity : 0.0;
             }
 
-            if (_shape == 0.0 && _invScale == 0.0)
+            if (_shape == 0.0 && _rate == 0.0)
             {
                 return 0.0;
             }
 
             if (_shape == 1.0)
             {
-                return _invScale*Math.Exp(-_invScale*x);
+                return _rate*Math.Exp(-_rate*x);
             }
 
-            return Math.Pow(_invScale, _shape)*Math.Pow(x, _shape - 1.0)*Math.Exp(-_invScale*x)/SpecialFunctions.Gamma(_shape);
+            return Math.Pow(_rate, _shape)*Math.Pow(x, _shape - 1.0)*Math.Exp(-_rate*x)/SpecialFunctions.Gamma(_shape);
         }
 
         /// <summary>
@@ -371,22 +367,22 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the log density at <paramref name="x"/>.</returns>
         public double DensityLn(double x)
         {
-            if (Double.IsPositiveInfinity(_invScale))
+            if (Double.IsPositiveInfinity(_rate))
             {
                 return x == _shape ? Double.PositiveInfinity : Double.NegativeInfinity;
             }
 
-            if (_shape == 0.0 && _invScale == 0.0)
+            if (_shape == 0.0 && _rate == 0.0)
             {
                 return Double.NegativeInfinity;
             }
 
             if (_shape == 1.0)
             {
-                return Math.Log(_invScale) - (_invScale*x);
+                return Math.Log(_rate) - (_rate*x);
             }
 
-            return (_shape*Math.Log(_invScale)) + ((_shape - 1.0)*Math.Log(x)) - (_invScale*x) - SpecialFunctions.GammaLn(_shape);
+            return (_shape*Math.Log(_rate)) + ((_shape - 1.0)*Math.Log(x)) - (_rate*x) - SpecialFunctions.GammaLn(_shape);
         }
 
         /// <summary>
@@ -396,32 +392,32 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
         public double CumulativeDistribution(double x)
         {
-            if (Double.IsPositiveInfinity(_invScale))
+            if (Double.IsPositiveInfinity(_rate))
             {
                 return x >= _shape ? 1.0 : 0.0;
             }
 
-            if (_shape == 0.0 && _invScale == 0.0)
+            if (_shape == 0.0 && _rate == 0.0)
             {
                 return 0.0;
             }
 
-            return SpecialFunctions.GammaLowerRegularized(_shape, x*_invScale);
+            return SpecialFunctions.GammaLowerRegularized(_shape, x*_rate);
         }
 
         /// <summary>
         /// <para>Sampling implementation based on:
         /// "A Simple Method for Generating Gamma Variables" - Marsaglia &amp; Tsang
-        /// ACM Transactions on Mathematical Software, Vol. 26, No. 3, September 2000, Pages 363–372.</para>
+        /// ACM Transactions on Mathematical Software, Vol. 26, No. 3, September 2000, Pages 363–372.</para>
         /// <para>This method performs no parameter checks.</para>
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="shape">The shape of the Gamma distribution.</param>
-        /// <param name="invScale">The inverse scale of the Gamma distribution.</param>
+        /// <param name="shape">The shape (k, α) of the Gamma distribution.</param>
+        /// <param name="rate">The rate or inverse scale (β) of the Gamma distribution.</param>
         /// <returns>A sample from a Gamma distributed random variable.</returns>
-        internal static double SampleUnchecked(System.Random rnd, double shape, double invScale)
+        internal static double SampleUnchecked(System.Random rnd, double shape, double rate)
         {
-            if (Double.IsPositiveInfinity(invScale))
+            if (Double.IsPositiveInfinity(rate))
             {
                 return shape;
             }
@@ -453,12 +449,12 @@ namespace MathNet.Numerics.Distributions
                 x = x*x;
                 if (u < 1.0 - (0.0331*x*x))
                 {
-                    return alphafix*d*v/invScale;
+                    return alphafix*d*v/rate;
                 }
 
                 if (Math.Log(u) < (0.5*x) + (d*(1.0 - v + Math.Log(v))))
                 {
-                    return alphafix*d*v/invScale;
+                    return alphafix*d*v/rate;
                 }
             }
         }
@@ -469,7 +465,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a sample from the distribution.</returns>
         public double Sample()
         {
-            return SampleUnchecked(RandomSource, _shape, _invScale);
+            return SampleUnchecked(RandomSource, _shape, _rate);
         }
 
         /// <summary>
@@ -480,7 +476,7 @@ namespace MathNet.Numerics.Distributions
         {
             while (true)
             {
-                yield return SampleUnchecked(RandomSource, _shape, _invScale);
+                yield return SampleUnchecked(RandomSource, _shape, _rate);
             }
         }
 
@@ -488,36 +484,36 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sample from the Gamma distribution.
         /// </summary>
         /// <param name="rng">The random number generator to use.</param>
-        /// <param name="shape">The shape of the Gamma distribution from which to generate samples.</param>
-        /// <param name="invScale">The inverse scale of the Gamma distribution from which to generate samples.</param>
+        /// <param name="shape">The shape (k, α) of the Gamma distribution.</param>
+        /// <param name="rate">The rate or inverse scale (β) of the Gamma distribution.</param>
         /// <returns>a sample from the distribution.</returns>
-        public static double Sample(System.Random rng, double shape, double invScale)
+        public static double Sample(System.Random rng, double shape, double rate)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(shape, invScale))
+            if (Control.CheckDistributionParameters && !IsValidParameterSet(shape, rate))
             {
                 throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
             }
 
-            return SampleUnchecked(rng, shape, invScale);
+            return SampleUnchecked(rng, shape, rate);
         }
 
         /// <summary>
         /// Generates a sequence of samples from the Gamma distribution.
         /// </summary>
         /// <param name="rng">The random number generator to use.</param>
-        /// <param name="shape">The shape of the Gamma distribution from which to generate samples.</param>
-        /// <param name="invScale">The inverse scale of the Gamma distribution from which to generate samples.</param>
+        /// <param name="shape">The shape (k, α) of the Gamma distribution.</param>
+        /// <param name="rate">The rate or inverse scale (β) of the Gamma distribution.</param>
         /// <returns>a sequence of samples from the distribution.</returns>
-        public static IEnumerable<double> Samples(System.Random rng, double shape, double invScale)
+        public static IEnumerable<double> Samples(System.Random rng, double shape, double rate)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(shape, invScale))
+            if (Control.CheckDistributionParameters && !IsValidParameterSet(shape, rate))
             {
                 throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
             }
 
             while (true)
             {
-                yield return SampleUnchecked(rng, shape, invScale);
+                yield return SampleUnchecked(rng, shape, rate);
             }
         }
     }

src/Numerics/Distributions/Geometric.cs

@@ -111,22 +111,21 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
+        /// Gets or sets the probability of generating a one.
         /// </summary>
-        public System.Random RandomSource
+        public double P
         {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
+            get { return _p; }
+            set { SetParameters(value); }
         }
 
         /// <summary>
-        /// Gets or sets the probability of generating a one.
+        /// Gets or sets the random number generator which is used to draw random samples.
         /// </summary>
-        public double P
+        public System.Random RandomSource
         {
-            get { return _p; }
-
-            set { SetParameters(value); }
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
         }
 
         /// <summary>

src/Numerics/Distributions/Hypergeometric.cs

@@ -51,19 +51,8 @@ namespace MathNet.Numerics.Distributions
     {
         System.Random _random;
 
-        /// <summary>
-        /// The size of the population (N).
-        /// </summary>
         int _population;
-
-        /// <summary>
-        /// The number successes within the population (K, M).
-        /// </summary>
         int _success;
-
-        /// <summary>
-        /// The number of draws without replacement (n).
-        /// </summary>
         int _draws;
 
         /// <summary>

src/Numerics/Distributions/InverseGamma.cs

@@ -38,7 +38,7 @@ namespace MathNet.Numerics.Distributions
     /// Continuous Univariate Inverse Gamma distribution.
     /// The inverse Gamma distribution is a distribution over the positive real numbers parameterized by
     /// two positive parameters.
-    /// <a href="http://en.wikipedia.org/wiki/inverse-gamma_distribution">Wikipedia - InverseGamma distribution</a>.
+    /// <a href="http://en.wikipedia.org/wiki/Inverse-gamma_distribution">Wikipedia - InverseGamma distribution</a>.
     /// </summary>
     /// <remarks><para>The distribution will use the <see cref="System.Random"/> by default. 
     /// Users can set the random number generator by using the <see cref="RandomSource"/> property.</para>
@@ -55,8 +55,8 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Initializes a new instance of the <see cref="InverseGamma"/> class. 
         /// </summary>
-        /// <param name="shape">The shape (alpha) parameter of the inverse Gamma distribution.</param>
-        /// <param name="scale">The scale (beta) parameter of the inverse Gamma distribution.</param>
+        /// <param name="shape">The shape (α) of the inverse Gamma distribution.</param>
+        /// <param name="scale">The scale (β) of the inverse Gamma distribution.</param>
         public InverseGamma(double shape, double scale)
         {
             _random = new System.Random();
@@ -66,8 +66,8 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Initializes a new instance of the <see cref="InverseGamma"/> class. 
         /// </summary>
-        /// <param name="shape">The shape (alpha) parameter of the inverse Gamma distribution.</param>
-        /// <param name="scale">The scale (beta) parameter of the inverse Gamma distribution.</param>
+        /// <param name="shape">The shape (α) of the inverse Gamma distribution.</param>
+        /// <param name="scale">The scale (β) of the inverse Gamma distribution.</param>
         /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
         public InverseGamma(double shape, double scale, System.Random randomSource)
         {
@@ -81,14 +81,14 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a string representation of the distribution.</returns>
         public override string ToString()
         {
-            return "InverseGamma(Shape = " + _shape + ", Inverse Scale = " + _scale + ")";
+            return "InverseGamma(α = " + _shape + ", β = " + _scale + ")";
         }
 
         /// <summary>
         /// Checks whether the parameters of the distribution are valid. 
         /// </summary>
-        /// <param name="shape">The shape (alpha) parameter of the inverse Gamma distribution.</param>
-        /// <param name="scale">The scale (beta) parameter of the inverse Gamma distribution.</param>
+        /// <param name="shape">The shape (α) of the inverse Gamma distribution.</param>
+        /// <param name="scale">The scale (β) of the inverse Gamma distribution.</param>
         /// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
         static bool IsValidParameterSet(double shape, double scale)
         {
@@ -98,8 +98,8 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Sets the parameters of the distribution after checking their validity.
         /// </summary>
-        /// <param name="shape">The shape (alpha) parameter of the inverse Gamma distribution.</param>
-        /// <param name="scale">The scale (beta) parameter of the inverse Gamma distribution.</param>
+        /// <param name="shape">The shape (α) of the inverse Gamma distribution.</param>
+        /// <param name="scale">The scale (β) of the inverse Gamma distribution.</param>
         /// <exception cref="ArgumentOutOfRangeException">When the parameters don't pass the <see cref="IsValidParameterSet"/> function.</exception>
         void SetParameters(double shape, double scale)
         {
@@ -113,16 +113,7 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
-        /// </summary>
-        public System.Random RandomSource
-        {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
-        }
-
-        /// <summary>
-        /// Gets or sets the shape (alpha) parameter.
+        /// Gets or sets the shape (α) parameter.
         /// </summary>
         public double Shape
         {
@@ -131,7 +122,7 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets The scale (beta) parameter.
+        /// Gets or sets The scale (β) parameter.
         /// </summary>
         public double Scale
         {
@@ -139,6 +130,15 @@ namespace MathNet.Numerics.Distributions
             set { SetParameters(_shape, value); }
         }
 
+        /// <summary>
+        /// Gets or sets the random number generator which is used to draw random samples.
+        /// </summary>
+        public System.Random RandomSource
+        {
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
+        }
+
         /// <summary>
         /// Gets the mean of the distribution.
         /// </summary>
@@ -275,8 +275,8 @@ namespace MathNet.Numerics.Distributions
         /// Samples the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="shape">The shape (alpha) parameter of the inverse Gamma distribution.</param>
-        /// <param name="scale">The scale (beta) parameter of the inverse Gamma distribution.</param>
+        /// <param name="shape">The shape (α) of the inverse Gamma distribution.</param>
+        /// <param name="scale">The scale (β) of the inverse Gamma distribution.</param>
         /// <returns>a random number from the distribution.</returns>
         internal static double SampleUnchecked(System.Random rnd, double shape, double scale)
         {
@@ -308,8 +308,8 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sample from the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="shape">The shape (alpha) parameter of the inverse Gamma distribution.</param>
-        /// <param name="scale">The scale (beta) parameter of the inverse Gamma distribution.</param>
+        /// <param name="shape">The shape (α) of the inverse Gamma distribution.</param>
+        /// <param name="scale">The scale (β) of the inverse Gamma distribution.</param>
         /// <returns>a sample from the distribution.</returns>
         public static double Sample(System.Random rnd, double shape, double scale)
         {
@@ -325,8 +325,8 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sequence of samples from the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="shape">The shape (alpha) parameter of the inverse Gamma distribution.</param>
-        /// <param name="scale">The scale (beta) parameter of the inverse Gamma distribution.</param>
+        /// <param name="shape">The shape (α) of the inverse Gamma distribution.</param>
+        /// <param name="scale">The scale (β) of the inverse Gamma distribution.</param>
         /// <returns>a sequence of samples from the distribution.</returns>
         public static IEnumerable<double> Samples(System.Random rnd, double shape, double scale)
         {

src/Numerics/Distributions/InverseWishart.cs

@@ -50,15 +50,8 @@ namespace MathNet.Numerics.Distributions
     {
         System.Random _random;
 
-        /// <summary>
-        /// The degrees of freedom for the inverse Wishart distribution.
-        /// </summary>
-        double _nu;
-
-        /// <summary>
-        /// The scale matrix for the inverse Wishart distribution.
-        /// </summary>
-        Matrix<double> _s;
+        double _freedom;
+        Matrix<double> _scale;
 
         /// <summary>
         /// Caches the Cholesky factorization of the scale matrix.
@@ -68,24 +61,24 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Initializes a new instance of the <see cref="InverseWishart"/> class. 
         /// </summary>
-        /// <param name="nu">The degrees of freedom for the inverse Wishart distribution.</param>
-        /// <param name="s">The scale matrix for the inverse Wishart distribution.</param>
-        public InverseWishart(double nu, Matrix<double> s)
+        /// <param name="degreeOfFreedom">The degree of freedom (ν) for the inverse Wishart distribution.</param>
+        /// <param name="scale">The scale matrix (Ψ) for the inverse Wishart distribution.</param>
+        public InverseWishart(double degreeOfFreedom, Matrix<double> scale)
         {
             _random = new System.Random();
-            SetParameters(nu, s);
+            SetParameters(degreeOfFreedom, scale);
         }
 
         /// <summary>
         /// Initializes a new instance of the <see cref="InverseWishart"/> class. 
         /// </summary>
-        /// <param name="nu">The degrees of freedom for the inverse Wishart distribution.</param>
-        /// <param name="s">The scale matrix for the inverse Wishart distribution.</param>
+        /// <param name="degreeOfFreedom">The degree of freedom (ν) for the inverse Wishart distribution.</param>
+        /// <param name="scale">The scale matrix (Ψ) for the inverse Wishart distribution.</param>
         /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
-        public InverseWishart(double nu, Matrix<double> s, System.Random randomSource)
+        public InverseWishart(double degreeOfFreedom, Matrix<double> scale, System.Random randomSource)
         {
             _random = randomSource ?? new System.Random();
-            SetParameters(nu, s);
+            SetParameters(degreeOfFreedom, scale);
         }
 
         /// <summary>
@@ -94,76 +87,76 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a string representation of the distribution.</returns>
         public override string ToString()
         {
-            return "InverseWishart(Nu = " + _nu + ", Rows = " + _s.RowCount + ", Columns = " + _s.ColumnCount + ")";
+            return "InverseWishart(ν = " + _freedom + ", Rows = " + _scale.RowCount + ", Columns = " + _scale.ColumnCount + ")";
         }
 
         /// <summary>
         /// Checks whether the parameters of the distribution are valid. 
         /// </summary>
-        /// <param name="nu">The degrees of freedom for the Wishart distribution.</param>
-        /// <param name="s">The scale matrix for the Wishart distribution.</param>
+        /// <param name="degreeOfFreedom">The degree of freedom (ν) for the inverse Wishart distribution.</param>
+        /// <param name="scale">The scale matrix (Ψ) for the inverse Wishart distribution.</param>
         /// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
-        static bool IsValidParameterSet(double nu, Matrix<double> s)
+        static bool IsValidParameterSet(double degreeOfFreedom, Matrix<double> scale)
         {
-            if (s.RowCount != s.ColumnCount)
+            if (scale.RowCount != scale.ColumnCount)
             {
                 return false;
             }
 
-            for (var i = 0; i < s.RowCount; i++)
+            for (var i = 0; i < scale.RowCount; i++)
             {
-                if (s.At(i, i) <= 0.0)
+                if (scale.At(i, i) <= 0.0)
                 {
                     return false;
                 }
             }
 
-            return nu > 0.0;
+            return degreeOfFreedom > 0.0;
         }
 
         /// <summary>
         /// Sets the parameters of the distribution after checking their validity.
         /// </summary>
-        /// <param name="nu">The degrees of freedom for the Wishart distribution.</param>
-        /// <param name="s">The scale matrix for the Wishart distribution.</param>
+        /// <param name="degreeOfFreedom">The degree of freedom (ν) for the inverse Wishart distribution.</param>
+        /// <param name="scale">The scale matrix (Ψ) for the inverse Wishart distribution.</param>
         /// <exception cref="ArgumentOutOfRangeException">When the parameters don't pass the <see cref="IsValidParameterSet"/> function.</exception>
-        void SetParameters(double nu, Matrix<double> s)
+        void SetParameters(double degreeOfFreedom, Matrix<double> scale)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(nu, s))
+            if (Control.CheckDistributionParameters && !IsValidParameterSet(degreeOfFreedom, scale))
             {
                 throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
             }
 
-            _nu = nu;
-            _s = s;
-            _chol = Cholesky<double>.Create(_s);
+            _freedom = degreeOfFreedom;
+            _scale = scale;
+            _chol = Cholesky<double>.Create(_scale);
         }
 
         /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
+        /// Gets or sets the degree of freedom (ν) for the inverse Wishart distribution.
         /// </summary>
-        public System.Random RandomSource
+        public double DegreeOfFreedom
         {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
+            get { return _freedom; }
+            set { SetParameters(value, _scale); }
         }
 
         /// <summary>
-        /// Gets or sets the degrees of freedom for the inverse Wishart distribution.
+        /// Gets or sets the scale matrix (Ψ) for the inverse Wishart distribution.
         /// </summary>
-        public double Nu
+        public Matrix<double> Scale
         {
-            get { return _nu; }
-            set { SetParameters(value, _s); }
+            get { return _scale; }
+            set { SetParameters(_freedom, value); }
         }
 
         /// <summary>
-        /// Gets or sets the scale matrix for the inverse Wishart distribution.
+        /// Gets or sets the random number generator which is used to draw random samples.
         /// </summary>
-        public Matrix<double> S
+        public System.Random RandomSource
         {
-            get { return _s; }
-            set { SetParameters(_nu, value); }
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
         }
 
         /// <summary>
@@ -172,7 +165,7 @@ namespace MathNet.Numerics.Distributions
         /// <value>The mean of the distribution.</value>
         public Matrix<double> Mean
         {
-            get { return _s*(1.0/(_nu - _s.RowCount - 1.0)); }
+            get { return _scale*(1.0/(_freedom - _scale.RowCount - 1.0)); }
         }
 
         /// <summary>
@@ -182,7 +175,7 @@ namespace MathNet.Numerics.Distributions
         /// <remarks>A. O'Hagan, and J. J. Forster (2004). Kendall's Advanced Theory of Statistics: Bayesian Inference. 2B (2 ed.). Arnold. ISBN 0-340-80752-0.</remarks>
         public Matrix<double> Mode
         {
-            get { return _s*(1.0/(_nu + _s.RowCount + 1.0)); }
+            get { return _scale*(1.0/(_freedom + _scale.RowCount + 1.0)); }
         }
 
         /// <summary>
@@ -194,13 +187,13 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                var res = _s.CreateMatrix(_s.RowCount, _s.ColumnCount);
+                var res = _scale.CreateMatrix(_scale.RowCount, _scale.ColumnCount);
                 for (var i = 0; i < res.RowCount; i++)
                 {
                     for (var j = 0; j < res.ColumnCount; j++)
                     {
-                        var num1 = ((_nu - _s.RowCount + 1)*_s.At(i, j)*_s.At(i, j)) + ((_nu - _s.RowCount - 1)*_s.At(i, i)*_s.At(j, j));
-                        var num2 = (_nu - _s.RowCount)*(_nu - _s.RowCount - 1)*(_nu - _s.RowCount - 1)*(_nu - _s.RowCount - 3);
+                        var num1 = ((_freedom - _scale.RowCount + 1)*_scale.At(i, j)*_scale.At(i, j)) + ((_freedom - _scale.RowCount - 1)*_scale.At(i, i)*_scale.At(j, j));
+                        var num2 = (_freedom - _scale.RowCount)*(_freedom - _scale.RowCount - 1)*(_freedom - _scale.RowCount - 1)*(_freedom - _scale.RowCount - 3);
                         res.At(i, j, num1/num2);
                     }
                 }
@@ -217,7 +210,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the density at <paramref name="x"/>.</returns>
         public double Density(Matrix<double> x)
         {
-            var p = _s.RowCount;
+            var p = _scale.RowCount;
 
             if (x.RowCount != p || x.ColumnCount != p)
             {
@@ -226,19 +219,19 @@ namespace MathNet.Numerics.Distributions
 
             var chol = Cholesky<double>.Create(x);
             var dX = chol.Determinant;
-            var sXi = chol.Solve(S);
+            var sXi = chol.Solve(Scale);
 
             // Compute the multivariate Gamma function.
             var gp = Math.Pow(Constants.Pi, p*(p - 1.0)/4.0);
             for (var j = 1; j <= p; j++)
             {
-                gp *= SpecialFunctions.Gamma((_nu + 1.0 - j)/2.0);
+                gp *= SpecialFunctions.Gamma((_freedom + 1.0 - j)/2.0);
             }
 
-            return Math.Pow(dX, -(_nu + p + 1.0)/2.0)
+            return Math.Pow(dX, -(_freedom + p + 1.0)/2.0)
                    *Math.Exp(-0.5*sXi.Trace())
-                   *Math.Pow(_chol.Determinant, _nu/2.0)
-                   /Math.Pow(2.0, _nu*p/2.0)
+                   *Math.Pow(_chol.Determinant, _freedom/2.0)
+                   /Math.Pow(2.0, _freedom*p/2.0)
                    /gp;
         }
 
@@ -249,7 +242,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a sample from the distribution.</returns>
         public Matrix<double> Sample()
         {
-            return Sample(RandomSource, _nu, _s);
+            return Sample(RandomSource, _freedom, _scale);
         }
 
         /// <summary>
@@ -257,17 +250,17 @@ namespace MathNet.Numerics.Distributions
         /// a Wishart random variable and inverting the matrix.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="nu">The degrees of freedom.</param>
-        /// <param name="s">The scale matrix.</param>
+        /// <param name="degreeOfFreedom">The degree of freedom (ν) for the inverse Wishart distribution.</param>
+        /// <param name="scale">The scale matrix (Ψ) for the inverse Wishart distribution.</param>
         /// <returns>a sample from the distribution.</returns>
-        public static Matrix<double> Sample(System.Random rnd, double nu, Matrix<double> s)
+        public static Matrix<double> Sample(System.Random rnd, double degreeOfFreedom, Matrix<double> scale)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(nu, s))
+            if (Control.CheckDistributionParameters && !IsValidParameterSet(degreeOfFreedom, scale))
             {
                 throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
             }
 
-            var r = Wishart.Sample(rnd, nu, s.Inverse());
+            var r = Wishart.Sample(rnd, degreeOfFreedom, scale.Inverse());
             return r.Inverse();
         }
     }

src/Numerics/Distributions/Laplace.cs

@@ -50,26 +50,9 @@ namespace MathNet.Numerics.Distributions
     {
         System.Random _random;
 
+        double _location;
         double _scale;
 
-        /// <summary>
-        /// Gets or sets the location of the Laplace distribution.
-        /// </summary>
-        public double Location
-        {
-            get { return Mean; }
-            set { SetParameters(value, _scale); }
-        }
-
-        /// <summary>
-        /// Gets or sets the scale of the Laplace distribution.
-        /// </summary>
-        public double Scale
-        {
-            get { return _scale; }
-            set { SetParameters(Mean, value); }
-        }
-
         /// <summary>
         /// Initializes a new instance of the <see cref="Laplace"/> class (location = 0, scale = 1). 
         /// </summary>
@@ -109,14 +92,14 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a string representation of the distribution.</returns>
         public override string ToString()
         {
-            return "Laplace(Location = " + Mean + ", Scale = " + _scale + ")";
+            return "Laplace(μ = " + _location + ", b = " + _scale + ")";
         }
 
         /// <summary>
         /// Checks whether the parameters of the distribution are valid. 
         /// </summary>
-        /// <param name="location">The location for the Laplace distribution.</param>
-        /// <param name="scale">The scale for the Laplace distribution.</param>
+        /// <param name="location">The location (μ) of the Laplace distribution.</param>
+        /// <param name="scale">The scale (b) of the Laplace distribution.</param>
         /// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
         static bool IsValidParameterSet(double location, double scale)
         {
@@ -126,8 +109,8 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Sets the parameters of the distribution after checking their validity.
         /// </summary>
-        /// <param name="location">The location for the Laplace distribution.</param>
-        /// <param name="scale">The scale for the Laplace distribution.</param>
+        /// <param name="location">The location (μ) of the Laplace distribution.</param>
+        /// <param name="scale">The scale (b) of the Laplace distribution.</param>
         /// <exception cref="ArgumentOutOfRangeException">When the parameters don't pass the <see cref="IsValidParameterSet"/> function.</exception>
         void SetParameters(double location, double scale)
         {
@@ -136,10 +119,28 @@ namespace MathNet.Numerics.Distributions
                 throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
             }
 
-            Mean = location;
+            _location = location;
             _scale = scale;
         }
 
+        /// <summary>
+        /// Gets or sets the location (μ) of the Laplace distribution.
+        /// </summary>
+        public double Location
+        {
+            get { return _location; }
+            set { SetParameters(value, _scale); }
+        }
+
+        /// <summary>
+        /// Gets or sets the scale (b) of the Laplace distribution.
+        /// </summary>
+        public double Scale
+        {
+            get { return _scale; }
+            set { SetParameters(_location, value); }
+        }
+
         /// <summary>
         /// Gets or sets the random number generator which is used to draw random samples.
         /// </summary>
@@ -152,7 +153,10 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Gets the mean of the distribution.
         /// </summary>
-        public double Mean { get; private set; }
+        public double Mean
+        {
+            get { return _location; }
+        }
 
         /// <summary>
         /// Gets the variance of the distribution.
@@ -191,7 +195,7 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         public double Mode
         {
-            get { return Mean; }
+            get { return _location; }
         }
 
         /// <summary>
@@ -199,7 +203,7 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         public double Median
         {
-            get { return Mean; }
+            get { return _location; }
         }
 
         /// <summary>
@@ -225,7 +229,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the density at <paramref name="x"/>.</returns>      
         public double Density(double x)
         {
-            return Math.Exp(-Math.Abs(x - Mean)/_scale)/(2.0*_scale);
+            return Math.Exp(-Math.Abs(x - _location)/_scale)/(2.0*_scale);
         }
 
         /// <summary>
@@ -245,15 +249,15 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
         public double CumulativeDistribution(double x)
         {
-            return 0.5*(1.0 + (Math.Sign(x - Mean)*(1.0 - Math.Exp(-Math.Abs(x - Mean)/_scale))));
+            return 0.5*(1.0 + (Math.Sign(x - _location)*(1.0 - Math.Exp(-Math.Abs(x - _location)/_scale))));
         }
 
         /// <summary>
         /// Samples the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="location">The location shape parameter.</param>
-        /// <param name="scale">The scale parameter.</param>
+        /// <param name="location">The location (μ) of the Laplace distribution.</param>
+        /// <param name="scale">The scale (b) of the Laplace distribution.</param>
         /// <returns>a random number from the distribution.</returns>
         internal static double SampleUnchecked(System.Random rnd, double location, double scale)
         {
@@ -267,7 +271,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a sample from the distribution.</returns>
         public double Sample()
         {
-            return SampleUnchecked(RandomSource, Mean, _scale);
+            return SampleUnchecked(RandomSource, _location, _scale);
         }
 
         /// <summary>
@@ -278,7 +282,7 @@ namespace MathNet.Numerics.Distributions
         {
             while (true)
             {
-                yield return SampleUnchecked(RandomSource, Mean, _scale);
+                yield return SampleUnchecked(RandomSource, _location, _scale);
             }
         }
 
@@ -286,8 +290,8 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sample from the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="location">The location shape parameter.</param>
-        /// <param name="scale">The scale parameter.</param>
+        /// <param name="location">The location (μ) of the Laplace distribution.</param>
+        /// <param name="scale">The scale (b) of the Laplace distribution.</param>
         /// <returns>a sample from the distribution.</returns>
         public static double Sample(System.Random rnd, double location, double scale)
         {
@@ -303,8 +307,8 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sequence of samples from the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="location">The location shape parameter.</param>
-        /// <param name="scale">The scale parameter.</param>
+        /// <param name="location">The location (μ) of the Laplace distribution.</param>
+        /// <param name="scale">The scale (b) of the Laplace distribution.</param>
         /// <returns>a sequence of samples from the distribution.</returns>
         public static IEnumerable<double> Samples(System.Random rnd, double location, double scale)
         {

src/Numerics/Distributions/LogNormal.cs

@@ -1,4 +1,4 @@
-// <copyright file="LogNormal.cs" company="Math.NET">
+// <copyright file="LogNormal.cs" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
@@ -58,8 +58,8 @@ namespace MathNet.Numerics.Distributions
         /// The distribution will be initialized with the default <seealso cref="System.Random"/>
         /// random number generator.
         /// </summary>
-        /// <param name="mu">The mu of the logarithm of the distribution.</param>
-        /// <param name="sigma">The standard deviation of the logarithm of the distribution.</param>
+        /// <param name="mu">The log-scale (μ) of the logarithm of the distribution.</param>
+        /// <param name="sigma">The shape (σ) of the logarithm of the distribution.</param>
         public LogNormal(double mu, double sigma)
         {
             _random = new System.Random();
@@ -71,8 +71,8 @@ namespace MathNet.Numerics.Distributions
         /// The distribution will be initialized with the default <seealso cref="System.Random"/>
         /// random number generator.
         /// </summary>
-        /// <param name="mu">The mu of the logarithm of the distribution.</param>
-        /// <param name="sigma">The standard deviation of the logarithm of the distribution.</param>
+        /// <param name="mu">The log-scale (μ) of the distribution.</param>
+        /// <param name="sigma">The shape (σ) of the distribution.</param>
         /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
         public LogNormal(double mu, double sigma, System.Random randomSource)
         {
@@ -108,14 +108,14 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a string representation of the distribution.</returns>
         public override string ToString()
         {
-            return "LogNormal(Mu = " + _mu + ", Sigma = " + _sigma + ")";
+            return "LogNormal(μ = " + _mu + ", σ = " + _sigma + ")";
         }
 
         /// <summary>
         /// Checks whether the parameters of the distribution are valid. 
         /// </summary>
-        /// <param name="mu">The mu of the logarithm of the distribution.</param>
-        /// <param name="sigma">The standard deviation of the logarithm of the distribution.</param>
+        /// <param name="mu">The log-scale (μ) of the distribution.</param>
+        /// <param name="sigma">The shape (σ) of the distribution.</param>
         /// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
         static bool IsValidParameterSet(double mu, double sigma)
         {
@@ -125,8 +125,8 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Sets the parameters of the distribution after checking their validity.
         /// </summary>
-        /// <param name="mu">The mu of the logarithm of the distribution.</param>
-        /// <param name="sigma">The standard deviation of the logarithm of the distribution.</param>
+        /// <param name="mu">The log-scale (μ) of the distribution.</param>
+        /// <param name="sigma">The shape (σ) of the distribution.</param>
         /// <exception cref="ArgumentOutOfRangeException">When the parameters don't pass the <see cref="IsValidParameterSet"/> function.</exception>
         void SetParameters(double mu, double sigma)
         {
@@ -140,16 +140,7 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
-        /// </summary>
-        public System.Random RandomSource
-        {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
-        }
-
-        /// <summary>
-        /// Gets or sets the mean of the logarithm of the log-normal.
+        /// Gets or sets the log-scale (μ) (mean of the logarithm) of the distribution.
         /// </summary>
         public double Mu
         {
@@ -158,7 +149,7 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets the standard deviation of the logarithm of the log-normal.
+        /// Gets or sets the shape (σ) (standard deviation of the logarithm) of the distribution.
         /// </summary>
         public double Sigma
         {
@@ -166,6 +157,15 @@ namespace MathNet.Numerics.Distributions
             set { SetParameters(_mu, value); }
         }
 
+        /// <summary>
+        /// Gets or sets the random number generator which is used to draw random samples.
+        /// </summary>
+        public System.Random RandomSource
+        {
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
+        }
+
         /// <summary>
         /// Gets the mu of the log-normal distribution.
         /// </summary>
@@ -324,8 +324,8 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sample from the log-normal distribution using the <i>Box-Muller</i> algorithm.
         /// </summary>
         /// <param name="rng">The random number generator to use.</param>
-        /// <param name="mu">The mu of the logarithm of the distribution.</param>
-        /// <param name="sigma">The standard deviation of the logarithm of the distribution.</param>
+        /// <param name="mu">The log-scale (μ) of the distribution.</param>
+        /// <param name="sigma">The shape (σ) of the distribution.</param>
         /// <returns>a sample from the distribution.</returns>
         public static double Sample(System.Random rng, double mu, double sigma)
         {
@@ -341,8 +341,8 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sequence of samples from the log-normal distribution using the <i>Box-Muller</i> algorithm.
         /// </summary>
         /// <param name="rng">The random number generator to use.</param>
-        /// <param name="mu">The mu of the logarithm of the distribution.</param>
-        /// <param name="sigma">The standard deviation of the logarithm of the distribution.</param>
+        /// <param name="mu">The log-scale (μ) of the distribution.</param>
+        /// <param name="sigma">The shape (σ) of the distribution.</param>
         /// <returns>a sequence of samples from the distribution.</returns>
         public static IEnumerable<double> Samples(System.Random rng, double mu, double sigma)
         {

src/Numerics/Distributions/MatrixNormal.cs

@@ -163,15 +163,6 @@ namespace MathNet.Numerics.Distributions
             _k = k;
         }
 
-        /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
-        /// </summary>
-        public System.Random RandomSource
-        {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
-        }
-
         /// <summary>
         /// Gets or sets the mean. (M)
         /// </summary>
@@ -202,6 +193,15 @@ namespace MathNet.Numerics.Distributions
             set { SetParameters(_m, _v, value); }
         }
 
+        /// <summary>
+        /// Gets or sets the random number generator which is used to draw random samples.
+        /// </summary>
+        public System.Random RandomSource
+        {
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
+        }
+
         /// <summary>
         /// Evaluates the probability density function for the matrix normal distribution.
         /// </summary>

src/Numerics/Distributions/Multinomial.cs

@@ -177,21 +177,12 @@ namespace MathNet.Numerics.Distributions
             _trials = n;
         }
 
-        /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
-        /// </summary>
-        public System.Random RandomSource
-        {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
-        }
-
         /// <summary>
         /// Gets or sets the proportion of ratios.
         /// </summary>
         public double[] P
         {
-            get { return (double[]) _p.Clone(); }
+            get { return (double[])_p.Clone(); }
             set { SetParameters(value, _trials); }
         }
 
@@ -204,6 +195,15 @@ namespace MathNet.Numerics.Distributions
             set { SetParameters(_p, value); }
         }
 
+        /// <summary>
+        /// Gets or sets the random number generator which is used to draw random samples.
+        /// </summary>
+        public System.Random RandomSource
+        {
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
+        }
+
         /// <summary>
         /// Gets the mean of the distribution.
         /// </summary>

src/Numerics/Distributions/NegativeBinomial.cs

@@ -51,30 +51,8 @@ namespace MathNet.Numerics.Distributions
         System.Random _random;
 
         double _trials;
-
-        /// <summary>
-        /// The p parameter of the distribution.
-        /// </summary>
         double _p;
 
-        /// <summary>
-        /// Gets or sets the number of trials.
-        /// </summary>
-        public double R
-        {
-            get { return _trials; }
-            set { SetParameters(value, _p); }
-        }
-
-        /// <summary>
-        /// Gets or sets the probability of success.
-        /// </summary>
-        public double P
-        {
-            get { return _p; }
-            set { SetParameters(_trials, value); }
-        }
-
         /// <summary>
         /// Initializes a new instance of the <see cref="NegativeBinomial"/> class. 
         /// </summary>
@@ -137,6 +115,24 @@ namespace MathNet.Numerics.Distributions
             _trials = r;
         }
 
+        /// <summary>
+        /// Gets or sets the number of trials.
+        /// </summary>
+        public double R
+        {
+            get { return _trials; }
+            set { SetParameters(value, _p); }
+        }
+
+        /// <summary>
+        /// Gets or sets the probability of success.
+        /// </summary>
+        public double P
+        {
+            get { return _p; }
+            set { SetParameters(_trials, value); }
+        }
+
         /// <summary>
         /// Gets or sets the random number generator which is used to draw random samples.
         /// </summary>

src/Numerics/Distributions/Normal.cs

@@ -1,4 +1,4 @@
-// <copyright file="Normal.cs" company="Math.NET">
+// <copyright file="Normal.cs" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
@@ -77,8 +77,8 @@ namespace MathNet.Numerics.Distributions
         /// Initializes a new instance of the Normal class with a particular mean and standard deviation. The distribution will
         /// be initialized with the default <seealso cref="System.Random"/> random number generator.
         /// </summary>
-        /// <param name="mean">The mean of the normal distribution.</param>
-        /// <param name="stddev">The standard deviation of the normal distribution.</param>
+        /// <param name="mean">The mean (μ) of the normal distribution.</param>
+        /// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
         public Normal(double mean, double stddev)
         {
             _random = new System.Random();
@@ -89,8 +89,8 @@ namespace MathNet.Numerics.Distributions
         /// Initializes a new instance of the Normal class with a particular mean and standard deviation. The distribution will
         /// be initialized with the default <seealso cref="System.Random"/> random number generator.
         /// </summary>
-        /// <param name="mean">The mean of the normal distribution.</param>
-        /// <param name="stddev">The standard deviation of the normal distribution.</param>
+        /// <param name="mean">The mean (μ) of the normal distribution.</param>
+        /// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
         /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
         public Normal(double mean, double stddev, System.Random randomSource)
         {
@@ -102,8 +102,8 @@ namespace MathNet.Numerics.Distributions
         /// Constructs a normal distribution from a mean and standard deviation. The distribution will
         /// be initialized with the default <seealso cref="System.Random"/> random number generator.
         /// </summary>
-        /// <param name="mean">The mean of the normal distribution.</param>
-        /// <param name="stddev">The standard deviation of the normal distribution.</param>
+        /// <param name="mean">The mean (μ) of the normal distribution.</param>
+        /// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
         /// <returns>a normal distribution.</returns>
         public static Normal WithMeanStdDev(double mean, double stddev)
         {
@@ -114,7 +114,7 @@ namespace MathNet.Numerics.Distributions
         /// Constructs a normal distribution from a mean and variance. The distribution will
         /// be initialized with the default <seealso cref="System.Random"/> random number generator.
         /// </summary>
-        /// <param name="mean">The mean of the normal distribution.</param>
+        /// <param name="mean">The mean (μ) of the normal distribution.</param>
         /// <param name="var">The variance of the normal distribution.</param>
         /// <returns>a normal distribution.</returns>
         public static Normal WithMeanVariance(double mean, double var)
@@ -126,7 +126,7 @@ namespace MathNet.Numerics.Distributions
         /// Constructs a normal distribution from a mean and precision. The distribution will
         /// be initialized with the default <seealso cref="System.Random"/> random number generator.
         /// </summary>
-        /// <param name="mean">The mean of the normal distribution.</param>
+        /// <param name="mean">The mean (μ) of the normal distribution.</param>
         /// <param name="precision">The precision of the normal distribution.</param>
         /// <returns>a normal distribution.</returns>
         public static Normal WithMeanPrecision(double mean, double precision)
@@ -149,14 +149,14 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a string representation of the distribution.</returns>
         public override string ToString()
         {
-            return "Normal(Mean = " + _mean + ", StdDev = " + _stdDev + ")";
+            return "Normal(μ = " + _mean + ", σ = " + _stdDev + ")";
         }
 
         /// <summary>
         /// Checks whether the parameters of the distribution are valid. 
         /// </summary>
-        /// <param name="mean">The mean of the normal distribution.</param>
-        /// <param name="stddev">The standard deviation of the normal distribution.</param>
+        /// <param name="mean">The mean (μ) of the normal distribution.</param>
+        /// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
         /// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
         static bool IsValidParameterSet(double mean, double stddev)
         {
@@ -166,8 +166,8 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Sets the parameters of the distribution after checking their validity.
         /// </summary>
-        /// <param name="mean">The mean of the normal distribution.</param>
-        /// <param name="stddev">The standard deviation of the normal distribution.</param>
+        /// <param name="mean">The mean (μ) of the normal distribution.</param>
+        /// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
         /// <exception cref="ArgumentOutOfRangeException">When the parameters don't pass the <see cref="IsValidParameterSet"/> function.</exception>
         void SetParameters(double mean, double stddev)
         {
@@ -181,12 +181,30 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
+        /// Gets or sets the mean (μ) of the normal distribution.
         /// </summary>
-        public System.Random RandomSource
+        public double Mean
         {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
+            get { return _mean; }
+            set { SetParameters(value, _stdDev); }
+        }
+
+        /// <summary>
+        /// Gets or sets the standard deviation (σ) of the normal distribution.
+        /// </summary>
+        public double StdDev
+        {
+            get { return _stdDev; }
+            set { SetParameters(_mean, value); }
+        }
+
+        /// <summary>
+        /// Gets or sets the variance of the normal distribution.
+        /// </summary>
+        public double Variance
+        {
+            get { return _stdDev * _stdDev; }
+            set { SetParameters(_mean, Math.Sqrt(value)); }
         }
 
         /// <summary>
@@ -194,47 +212,26 @@ namespace MathNet.Numerics.Distributions
         /// </summary>
         public double Precision
         {
-            get { return 1.0/(_stdDev*_stdDev); }
-
+            get { return 1.0 / (_stdDev * _stdDev); }
             set
             {
-                var sdev = 1.0/Math.Sqrt(value);
-
+                var sdev = 1.0 / Math.Sqrt(value);
                 // Handle the case when the precision is -0.
                 if (Double.IsInfinity(sdev))
                 {
                     sdev = Double.PositiveInfinity;
                 }
-
                 SetParameters(_mean, sdev);
             }
         }
 
         /// <summary>
-        /// Gets or sets the mean of the normal distribution.
-        /// </summary>
-        public double Mean
-        {
-            get { return _mean; }
-            set { SetParameters(value, _stdDev); }
-        }
-
-        /// <summary>
-        /// Gets or sets the variance of the normal distribution.
-        /// </summary>
-        public double Variance
-        {
-            get { return _stdDev*_stdDev; }
-            set { SetParameters(_mean, Math.Sqrt(value)); }
-        }
-
-        /// <summary>
-        /// Gets or sets the standard deviation of the normal distribution.
+        /// Gets or sets the random number generator which is used to draw random samples.
         /// </summary>
-        public double StdDev
+        public System.Random RandomSource
         {
-            get { return _stdDev; }
-            set { SetParameters(_mean, value); }
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
         }
 
         /// <summary>
@@ -288,27 +285,27 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Computes the density of the normal distribution (PDF), i.e. dP(X &lt;= x)/dx.
         /// </summary>
-        /// <param name="mean">The mean of the normal distribution.</param>
-        /// <param name="sdev">The standard deviation of the normal distribution.</param>
+        /// <param name="mean">The mean (μ) of the normal distribution.</param>
+        /// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
         /// <param name="x">The location at which to compute the density.</param>
         /// <returns>the density at <paramref name="x"/>.</returns>
-        internal static double Density(double mean, double sdev, double x)
+        internal static double Density(double mean, double stddev, double x)
         {
-            var d = (x - mean)/sdev;
-            return Math.Exp(-0.5*d*d)/(Constants.Sqrt2Pi*sdev);
+            var d = (x - mean)/stddev;
+            return Math.Exp(-0.5*d*d)/(Constants.Sqrt2Pi*stddev);
         }
 
         /// <summary>
         /// Computes the log density of the normal distribution (lnPDF), i.e. ln(dP(X &lt;= x)/dx).
         /// </summary>
-        /// <param name="mean">The mean of the normal distribution.</param>
-        /// <param name="sdev">The standard deviation of the normal distribution.</param>
+        /// <param name="mean">The mean (μ) of the normal distribution.</param>
+        /// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
         /// <param name="x">The location at which to compute the density.</param>
         /// <returns>the log density at <paramref name="x"/>.</returns>
-        internal static double DensityLn(double mean, double sdev, double x)
+        internal static double DensityLn(double mean, double stddev, double x)
         {
-            var d = (x - mean)/sdev;
-            return (-0.5*d*d) - Math.Log(sdev) - Constants.LogSqrt2Pi;
+            var d = (x - mean)/stddev;
+            return (-0.5*d*d) - Math.Log(stddev) - Constants.LogSqrt2Pi;
         }
 
         /// <summary>
@@ -334,13 +331,13 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Computes the cumulative distribution function (CDF) of the normal distribution, i.e. P(X &lt;= x).
         /// </summary>
-        /// <param name="mean">The mean of the normal distribution.</param>
-        /// <param name="sdev">The standard deviation of the normal distribution.</param>
+        /// <param name="mean">The mean (μ) of the normal distribution.</param>
+        /// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
         /// <param name="x">The location at which to compute the cumulative density.</param>
         /// <returns>the cumulative density at <paramref name="x"/>.</returns>
-        internal static double CumulativeDistribution(double mean, double sdev, double x)
+        internal static double CumulativeDistribution(double mean, double stddev, double x)
         {
-            return 0.5*(1.0 + SpecialFunctions.Erf((x - mean)/(sdev*Constants.Sqrt2)));
+            return 0.5*(1.0 + SpecialFunctions.Erf((x - mean)/(stddev*Constants.Sqrt2)));
         }
 
         /// <summary>
@@ -388,8 +385,8 @@ namespace MathNet.Numerics.Distributions
         /// Samples the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="mean">The mean of the normal distribution from which to generate samples.</param>
-        /// <param name="stddev">The standard deviation of the normal distribution from which to generate samples.</param>
+        /// <param name="mean">The mean (μ) of the normal distribution.</param>
+        /// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
         /// <returns>a random number from the distribution.</returns>
         internal static double SampleUnchecked(System.Random rnd, double mean, double stddev)
         {
@@ -423,8 +420,8 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sample from the normal distribution using the <i>Box-Muller</i> algorithm.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="mean">The mean of the normal distribution from which to generate samples.</param>
-        /// <param name="stddev">The standard deviation of the normal distribution from which to generate samples.</param>
+        /// <param name="mean">The mean (μ) of the normal distribution.</param>
+        /// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
         /// <returns>a sample from the distribution.</returns>
         public static double Sample(System.Random rnd, double mean, double stddev)
         {
@@ -440,8 +437,8 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sequence of samples from the normal distribution using the <i>Box-Muller</i> algorithm.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="mean">The mean of the normal distribution from which to generate samples.</param>
-        /// <param name="stddev">The standard deviation of the normal distribution from which to generate samples.</param>
+        /// <param name="mean">The mean (μ) of the normal distribution.</param>
+        /// <param name="stddev">The standard deviation (σ) of the normal distribution.</param>
         /// <returns>a sequence of samples from the distribution.</returns>
         public static IEnumerable<double> Samples(System.Random rnd, double mean, double stddev)
         {

src/Numerics/Distributions/NormalGamma.cs

@@ -180,15 +180,6 @@ namespace MathNet.Numerics.Distributions
             _precisionInvScale = precInvScale;
         }
 
-        /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
-        /// </summary>
-        public System.Random RandomSource
-        {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
-        }
-
         /// <summary>
         /// Gets or sets the location of the mean.
         /// </summary>
@@ -225,6 +216,15 @@ namespace MathNet.Numerics.Distributions
             set { SetParameters(_meanLocation, _meanScale, _precisionShape, value); }
         }
 
+        /// <summary>
+        /// Gets or sets the random number generator which is used to draw random samples.
+        /// </summary>
+        public System.Random RandomSource
+        {
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
+        }
+
         /// <summary>
         /// Returns the marginal distribution for the mean of the <c>NormalGamma</c> distribution.
         /// </summary>

src/Numerics/Distributions/Pareto.cs

@@ -56,8 +56,8 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Initializes a new instance of the <see cref="Pareto"/> class. 
         /// </summary>
-        /// <param name="scale">The scale parameter of the distribution.</param>
-        /// <param name="shape">The shape parameter of the distribution.</param>
+        /// <param name="scale">The scale (xm) of the distribution.</param>
+        /// <param name="shape">The shape (α) of the distribution.</param>
         /// <exception cref="ArgumentException">If <paramref name="scale"/> or <paramref name="shape"/> are negative.</exception>
         public Pareto(double scale, double shape)
         {
@@ -68,8 +68,8 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Initializes a new instance of the <see cref="Pareto"/> class. 
         /// </summary>
-        /// <param name="scale">The scale parameter of the distribution.</param>
-        /// <param name="shape">The shape parameter of the distribution.</param>
+        /// <param name="scale">The scale (xm) of the distribution.</param>
+        /// <param name="shape">The shape (α) of the distribution.</param>
         /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
         /// <exception cref="ArgumentException">If <paramref name="scale"/> or <paramref name="shape"/> are negative.</exception>
         public Pareto(double scale, double shape, System.Random randomSource)
@@ -84,14 +84,14 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a string representation of the distribution.</returns>
         public override string ToString()
         {
-            return "Pareto(Scale = " + _scale + ", Shape = " + _shape + ")";
+            return "Pareto(xm = " + _scale + ", α = " + _shape + ")";
         }
 
         /// <summary>
         /// Checks whether the parameters of the distribution are valid. 
         /// </summary>
-        /// <param name="scale">The scale parameter of the distribution.</param>
-        /// <param name="shape">The shape parameter of the distribution.</param>
+        /// <param name="scale">The scale (xm) of the distribution.</param>
+        /// <param name="shape">The shape (α) of the distribution.</param>
         /// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
         static bool IsValidParameterSet(double scale, double shape)
         {
@@ -101,8 +101,8 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Sets the parameters of the distribution after checking their validity.
         /// </summary>
-        /// <param name="scale">The scale parameter of the distribution.</param>
-        /// <param name="shape">The shape parameter of the distribution.</param>
+        /// <param name="scale">The scale (xm) of the distribution.</param>
+        /// <param name="shape">The shape (α) of the distribution.</param>
         /// <exception cref="ArgumentOutOfRangeException">When the parameters don't pass the <see cref="IsValidParameterSet"/> function.</exception>
         void SetParameters(double scale, double shape)
         {
@@ -116,16 +116,7 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
-        /// </summary>
-        public System.Random RandomSource
-        {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
-        }
-
-        /// <summary>
-        /// Gets or sets the scale parameter of the distribution.
+        /// Gets or sets the scale (xm) of the distribution.
         /// </summary>
         public double Scale
         {
@@ -134,7 +125,7 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets the shape parameter of the distribution.
+        /// Gets or sets the shape (α) of the distribution.
         /// </summary>
         public double Shape
         {
@@ -142,6 +133,15 @@ namespace MathNet.Numerics.Distributions
             set { SetParameters(_scale, value); }
         }
 
+        /// <summary>
+        /// Gets or sets the random number generator which is used to draw random samples.
+        /// </summary>
+        public System.Random RandomSource
+        {
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
+        }
+
         /// <summary>
         /// Gets the mean of the distribution.
         /// </summary>
@@ -264,8 +264,8 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sample from the Pareto distribution without doing parameter checking.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="scale">The scale parameter.</param>
-        /// <param name="shape">The shape parameter.</param>
+        /// <param name="scale">The scale (xm) of the distribution.</param>
+        /// <param name="shape">The shape (α) of the distribution.</param>
         /// <returns>a random number from the Pareto distribution.</returns>
         internal static double SampleUnchecked(System.Random rnd, double scale, double shape)
         {
@@ -297,8 +297,8 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sample from the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="scale">The scale parameter.</param>
-        /// <param name="shape">The shape parameter.</param>
+        /// <param name="scale">The scale (xm) of the distribution.</param>
+        /// <param name="shape">The shape (α) of the distribution.</param>
         /// <returns>a sample from the distribution.</returns>
         public static double Sample(System.Random rnd, double scale, double shape)
         {
@@ -314,8 +314,8 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sequence of samples from the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="scale">The scale parameter.</param>
-        /// <param name="shape">The shape parameter.</param>
+        /// <param name="scale">The scale (xm) of the distribution.</param>
+        /// <param name="shape">The shape (α) of the distribution.</param>
         /// <returns>a sequence of samples from the distribution.</returns>
         public static IEnumerable<double> Samples(System.Random rnd, double scale, double shape)
         {

src/Numerics/Distributions/Poisson.cs

@@ -48,15 +48,6 @@ namespace MathNet.Numerics.Distributions
 
         double _lambda;
 
-        /// <summary>
-        /// Gets or sets the Poisson distribution parameter λ.
-        /// </summary>
-        public double Lambda
-        {
-            get { return _lambda; }
-            set { SetParameters(value); }
-        }
-
         /// <summary>
         /// Initializes a new instance of the <see cref="Poisson"/> class.
         /// </summary>
@@ -116,6 +107,15 @@ namespace MathNet.Numerics.Distributions
             _lambda = lambda;
         }
 
+        /// <summary>
+        /// Gets or sets the Poisson distribution parameter λ.
+        /// </summary>
+        public double Lambda
+        {
+            get { return _lambda; }
+            set { SetParameters(value); }
+        }
+
         /// <summary>
         /// Gets or sets the random number generator which is used to draw random samples.
         /// </summary>

src/Numerics/Distributions/Rayleigh.cs

@@ -56,7 +56,7 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Initializes a new instance of the <see cref="Rayleigh"/> class. 
         /// </summary>
-        /// <param name="scale">The scale parameter of the distribution.</param>
+        /// <param name="scale">The scale (σ) of the distribution.</param>
         /// <exception cref="ArgumentException">If <paramref name="scale"/> is negative.</exception>
         public Rayleigh(double scale)
         {
@@ -67,7 +67,7 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Initializes a new instance of the <see cref="Rayleigh"/> class. 
         /// </summary>
-        /// <param name="scale">The scale parameter of the distribution.</param>
+        /// <param name="scale">The scale (σ) of the distribution.</param>
         /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
         /// <exception cref="ArgumentException">If <paramref name="scale"/> is negative.</exception>
         public Rayleigh(double scale, System.Random randomSource)
@@ -82,13 +82,13 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a string representation of the distribution.</returns>
         public override string ToString()
         {
-            return "Rayleigh(Scale = " + _scale + ")";
+            return "Rayleigh(σ = " + _scale + ")";
         }
 
         /// <summary>
         /// Checks whether the parameters of the distribution are valid. 
         /// </summary>
-        /// <param name="scale">The scale parameter of the distribution.</param>
+        /// <param name="scale">The scale (σ) of the distribution.</param>
         /// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
         static bool IsValidParameterSet(double scale)
         {
@@ -98,7 +98,7 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Sets the parameters of the distribution after checking their validity.
         /// </summary>
-        /// <param name="scale">The scale parameter of the distribution.</param>
+        /// <param name="scale">The scale (σ) of the distribution.</param>
         /// <exception cref="ArgumentOutOfRangeException">When the parameters don't pass the <see cref="IsValidParameterSet"/> function.</exception>
         void SetParameters(double scale)
         {
@@ -111,21 +111,21 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
+        /// Gets or sets the scale (σ) of the distribution.
         /// </summary>
-        public System.Random RandomSource
+        public double Scale
         {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
+            get { return _scale; }
+            set { SetParameters(value); }
         }
 
         /// <summary>
-        /// Gets or sets the scale parameter of the distribution.
+        /// Gets or sets the random number generator which is used to draw random samples.
         /// </summary>
-        public double Scale
+        public System.Random RandomSource
         {
-            get { return _scale; }
-            set { SetParameters(value); }
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
         }
 
         /// <summary>
@@ -234,7 +234,7 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sample from the Rayleigh distribution without doing parameter checking.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="scale">The scale parameter.</param>
+        /// <param name="scale">The scale (σ) of the distribution.</param>
         /// <returns>a random number from the Rayleigh distribution.</returns>
         internal static double SampleUnchecked(System.Random rnd, double scale)
         {
@@ -266,7 +266,7 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sample from the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="scale">The scale parameter.</param>
+        /// <param name="scale">The scale (σ) of the distribution.</param>
         /// <returns>a sample from the distribution.</returns>
         public static double Sample(System.Random rnd, double scale)
         {
@@ -282,7 +282,7 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sequence of samples from the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="scale">The scale parameter.</param>
+        /// <param name="scale">The scale (σ) of the distribution.</param>
         /// <returns>a sequence of samples from the distribution.</returns>
         public static IEnumerable<double> Samples(System.Random rnd, double scale)
         {

src/Numerics/Distributions/Stable.cs

@@ -51,26 +51,18 @@ namespace MathNet.Numerics.Distributions
     {
         System.Random _random;
 
-        /// <summary>
-        /// The stability parameter of the distribution.
-        /// </summary>
         double _alpha;
-
-        /// <summary>
-        /// The skewness parameter of the distribution.
-        /// </summary>
         double _beta;
-
         double _scale;
         double _location;
 
         /// <summary>
         /// Initializes a new instance of the <see cref="Stable"/> class. 
         /// </summary>
-        /// <param name="alpha">The stability parameter of the distribution.</param>
-        /// <param name="beta">The skewness parameter of the distribution.</param>
-        /// <param name="scale">The scale parameter of the distribution.</param>
-        /// <param name="location">The location parameter of the distribution.</param>
+        /// <param name="alpha">The stability (α) of the distribution.</param>
+        /// <param name="beta">The skewness (β) of the distribution.</param>
+        /// <param name="scale">The scale (c) of the distribution.</param>
+        /// <param name="location">The location (μ) of the distribution.</param>
         public Stable(double alpha, double beta, double scale, double location)
         {
             _random = new System.Random();
@@ -80,10 +72,10 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Initializes a new instance of the <see cref="Stable"/> class. 
         /// </summary>
-        /// <param name="alpha">The stability parameter of the distribution.</param>
-        /// <param name="beta">The skewness parameter of the distribution.</param>
-        /// <param name="scale">The scale parameter of the distribution.</param>
-        /// <param name="location">The location parameter of the distribution.</param>
+        /// <param name="alpha">The stability (α) of the distribution.</param>
+        /// <param name="beta">The skewness (β) of the distribution.</param>
+        /// <param name="scale">The scale (c) of the distribution.</param>
+        /// <param name="location">The location (μ) of the distribution.</param>
         /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
         public Stable(double alpha, double beta, double scale, double location, System.Random randomSource)
         {
@@ -97,16 +89,16 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a string representation of the distribution.</returns>
         public override string ToString()
         {
-            return "Stable(" + "Stability = " + _alpha + ", Skewness = " + _beta + ", Scale = " + _scale + ", Location = " + _location + ")";
+            return "Stable(α = " + _alpha + ", β = " + _beta + ", c = " + _scale + ", μ = " + _location + ")";
         }
 
         /// <summary>
         /// Checks whether the parameters of the distribution are valid. 
         /// </summary>
-        /// <param name="alpha">The stability parameter of the distribution.</param>
-        /// <param name="beta">The skewness parameter of the distribution.</param>
-        /// <param name="scale">The scale parameter of the distribution.</param>
-        /// <param name="location">The location parameter of the distribution.</param>
+        /// <param name="alpha">The stability (α) of the distribution.</param>
+        /// <param name="beta">The skewness (β) of the distribution.</param>
+        /// <param name="scale">The scale (c) of the distribution.</param>
+        /// <param name="location">The location (μ) of the distribution.</param>
         /// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
         static bool IsValidParameterSet(double alpha, double beta, double scale, double location)
         {
@@ -116,10 +108,10 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Sets the parameters of the distribution after checking their validity.
         /// </summary>
-        /// <param name="alpha">The stability parameter of the distribution.</param>
-        /// <param name="beta">The skewness parameter of the distribution.</param>
-        /// <param name="scale">The scale parameter of the distribution.</param>
-        /// <param name="location">The location parameter of the distribution.</param>
+        /// <param name="alpha">The stability (α) of the distribution.</param>
+        /// <param name="beta">The skewness (β) of the distribution.</param>
+        /// <param name="scale">The scale (c) of the distribution.</param>
+        /// <param name="location">The location (μ) of the distribution.</param>
         void SetParameters(double alpha, double beta, double scale, double location)
         {
             if (Control.CheckDistributionParameters && !IsValidParameterSet(alpha, beta, scale, location))
@@ -134,16 +126,7 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
-        /// </summary>
-        public System.Random RandomSource
-        {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
-        }
-
-        /// <summary>
-        /// Gets or sets the stability parameter of the distribution.
+        /// Gets or sets the stability (α) of the distribution.
         /// </summary>
         public double Alpha
         {
@@ -152,7 +135,7 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets The skewness parameter of the distribution.
+        /// Gets or sets The skewness (β) of the distribution.
         /// </summary>
         public double Beta
         {
@@ -161,7 +144,7 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets the scale parameter of the distribution.
+        /// Gets or sets the scale (c) of the distribution.
         /// </summary>
         public double Scale
         {
@@ -170,7 +153,7 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets the location parameter of the distribution.
+        /// Gets or sets the location (μ) of the distribution.
         /// </summary>
         public double Location
         {
@@ -178,6 +161,15 @@ namespace MathNet.Numerics.Distributions
             set { SetParameters(_alpha, _beta, _scale, value); }
         }
 
+        /// <summary>
+        /// Gets or sets the random number generator which is used to draw random samples.
+        /// </summary>
+        public System.Random RandomSource
+        {
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
+        }
+
         /// <summary>
         /// Gets the mean of the distribution.
         /// </summary>
@@ -338,8 +330,8 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Computes the density of the Levy distribution.
         /// </summary>
-        /// <param name="scale">The scale parameter of the distribution.</param>
-        /// <param name="location">The location parameter of the distribution.</param>
+        /// <param name="scale">The scale (c) of the distribution.</param>
+        /// <param name="location">The location (μ) of the distribution.</param>
         /// <param name="x">The location at which to compute the density.</param>
         /// <returns>the density at <paramref name="x"/>.</returns>
         static double LevyDensity(double scale, double location, double x)
@@ -392,8 +384,8 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Computes the cumulative distribution function of the Levy distribution.
         /// </summary>
-        /// <param name="scale">The scale parameter.</param>
-        /// <param name="location">The location parameter.</param>
+        /// <param name="scale">The scale (c) of the distribution.</param>
+        /// <param name="location">The location (μ) of the distribution.</param>
         /// <param name="x">The location at which to compute the cumulative density.</param>
         /// <returns>the cumulative density at <paramref name="x"/>.</returns>
         static double LevyCumulativeDistribution(double scale, double location, double x)
@@ -406,10 +398,10 @@ namespace MathNet.Numerics.Distributions
         /// Samples the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="alpha">The stability parameter of the distribution.</param>
-        /// <param name="beta">The skewness parameter of the distribution.</param>
-        /// <param name="scale">The scale parameter of the distribution.</param>
-        /// <param name="location">The location parameter of the distribution.</param>
+        /// <param name="alpha">The stability (α) of the distribution.</param>
+        /// <param name="beta">The skewness (β) of the distribution.</param>
+        /// <param name="scale">The scale (c) of the distribution.</param>
+        /// <param name="location">The location (μ) of the distribution.</param>
         /// <returns>a random number from the distribution.</returns>
         internal static double SampleUnchecked(System.Random rnd, double alpha, double beta, double scale, double location)
         {
@@ -464,10 +456,10 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sample from the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="alpha">The stability parameter of the distribution.</param>
-        /// <param name="beta">The skewness parameter of the distribution.</param>
-        /// <param name="scale">The scale parameter of the distribution.</param>
-        /// <param name="location">The location parameter of the distribution.</param>
+        /// <param name="alpha">The stability (α) of the distribution.</param>
+        /// <param name="beta">The skewness (β) of the distribution.</param>
+        /// <param name="scale">The scale (c) of the distribution.</param>
+        /// <param name="location">The location (μ) of the distribution.</param>
         /// <returns>a sample from the distribution.</returns>
         public static double Sample(System.Random rnd, double alpha, double beta, double scale, double location)
         {
@@ -483,10 +475,10 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sequence of samples from the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="alpha">The stability parameter of the distribution.</param>
-        /// <param name="beta">The skewness parameter of the distribution.</param>
-        /// <param name="scale">The scale parameter of the distribution.</param>
-        /// <param name="location">The location parameter of the distribution.</param>
+        /// <param name="alpha">The stability (α) of the distribution.</param>
+        /// <param name="beta">The skewness (β) of the distribution.</param>
+        /// <param name="scale">The scale (c) of the distribution.</param>
+        /// <param name="location">The location (μ) of the distribution.</param>
         /// <returns>a sequence of samples from the distribution.</returns>
         public static IEnumerable<double> Samples(System.Random rnd, double alpha, double beta, double scale, double location)
         {

src/Numerics/Distributions/StudentT.cs

@@ -142,15 +142,6 @@ namespace MathNet.Numerics.Distributions
             _freedom = dof;
         }
 
-        /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
-        /// </summary>
-        public System.Random RandomSource
-        {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
-        }
-
         /// <summary>
         /// Gets or sets the location of the Student t-distribution.
         /// </summary>
@@ -178,6 +169,15 @@ namespace MathNet.Numerics.Distributions
             set { SetParameters(_location, _scale, value); }
         }
 
+        /// <summary>
+        /// Gets or sets the random number generator which is used to draw random samples.
+        /// </summary>
+        public System.Random RandomSource
+        {
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
+        }
+
         /// <summary>
         /// Gets the mean of the Student t-distribution.
         /// </summary>

src/Numerics/Distributions/Weibull.cs

@@ -1,4 +1,4 @@
-// <copyright file="Weibull.cs" company="Math.NET">
+// <copyright file="Weibull.cs" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
@@ -65,8 +65,8 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Initializes a new instance of the Weibull class.
         /// </summary>
-        /// <param name="shape">The shape of the Weibull distribution.</param>
-        /// <param name="scale">The inverse scale of the Weibull distribution.</param>
+        /// <param name="shape">The shape (k) of the Weibull distribution.</param>
+        /// <param name="scale">The scale (λ) of the Weibull distribution.</param>
         public Weibull(double shape, double scale)
         {
             _random = new System.Random();
@@ -76,8 +76,8 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Initializes a new instance of the Weibull class.
         /// </summary>
-        /// <param name="shape">The shape of the Weibull distribution.</param>
-        /// <param name="scale">The inverse scale of the Weibull distribution.</param>
+        /// <param name="shape">The shape (k) of the Weibull distribution.</param>
+        /// <param name="scale">The scale (λ) of the Weibull distribution.</param>
         /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
         public Weibull(double shape, double scale, System.Random randomSource)
         {
@@ -91,14 +91,14 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a string representation of the distribution.</returns>
         public override string ToString()
         {
-            return "Weibull(Shape = " + _shape + ", Scale = " + _scale + ")";
+            return "Weibull(k = " + _shape + ", λ = " + _scale + ")";
         }
 
         /// <summary>
         /// Checks whether the parameters of the distribution are valid. 
         /// </summary>
-        /// <param name="shape">The shape of the Weibull distribution.</param>
-        /// <param name="scale">The scale of the Weibull distribution.</param>
+        /// <param name="shape">The shape (k) of the Weibull distribution.</param>
+        /// <param name="scale">The scale (λ) of the Weibull distribution.</param>
         /// <returns><c>true</c> when the parameters positive valid floating point numbers, <c>false</c> otherwise.</returns>
         static bool IsValidParameterSet(double shape, double scale)
         {
@@ -108,8 +108,8 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Sets the parameters of the distribution after checking their validity.
         /// </summary>
-        /// <param name="shape">The shape of the Weibull distribution.</param>
-        /// <param name="scale">The inverse scale of the Weibull distribution.</param>
+        /// <param name="shape">The shape (k) of the Weibull distribution.</param>
+        /// <param name="scale">The scale (λ) of the Weibull distribution.</param>
         /// <exception cref="ArgumentOutOfRangeException">When the parameters don't pass the <see cref="IsValidParameterSet"/> function.</exception>
         void SetParameters(double shape, double scale)
         {
@@ -124,16 +124,7 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
-        /// </summary>
-        public System.Random RandomSource
-        {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
-        }
-
-        /// <summary>
-        /// Gets or sets the shape of the Weibull distribution.
+        /// Gets or sets the shape (k) of the Weibull distribution.
         /// </summary>
         public double Shape
         {
@@ -142,7 +133,7 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets the scale of the Weibull distribution.
+        /// Gets or sets the scale (λ) of the Weibull distribution.
         /// </summary>
         public double Scale
         {
@@ -150,6 +141,15 @@ namespace MathNet.Numerics.Distributions
             set { SetParameters(_shape, value); }
         }
 
+        /// <summary>
+        /// Gets or sets the random number generator which is used to draw random samples.
+        /// </summary>
+        public System.Random RandomSource
+        {
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
+        }
+
         /// <summary>
         /// Gets the mean of the Weibull distribution.
         /// </summary>
@@ -297,8 +297,8 @@ namespace MathNet.Numerics.Distributions
         /// any parameter checks.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="shape">The shape of the Weibull distribution.</param>
-        /// <param name="scale">The scale of the Weibull distribution.</param>
+        /// <param name="shape">The shape (k) of the Weibull distribution.</param>
+        /// <param name="scale">The scale (λ) of the Weibull distribution.</param>
         /// <returns>A sample from a Weibull distributed random variable.</returns>
         internal static double SampleUnchecked(System.Random rnd, double shape, double scale)
         {
@@ -331,8 +331,8 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sample from the Weibull distribution.
         /// </summary>
         /// <param name="rng">The random number generator to use.</param>
-        /// <param name="shape">The shape of the Weibull distribution from which to generate samples.</param>
-        /// <param name="scale">The scale of the Weibull distribution from which to generate samples.</param>
+        /// <param name="shape">The shape (k) of the Weibull distribution.</param>
+        /// <param name="scale">The scale (λ) of the Weibull distribution.</param>
         /// <returns>a sample from the distribution.</returns>
         public static double Sample(System.Random rng, double shape, double scale)
         {
@@ -348,8 +348,8 @@ namespace MathNet.Numerics.Distributions
         /// Generates a sequence of samples from the Weibull distribution.
         /// </summary>
         /// <param name="rng">The random number generator to use.</param>
-        /// <param name="shape">The shape of the Weibull distribution from which to generate samples.</param>
-        /// <param name="scale">The scale of the Weibull distribution from which to generate samples.</param>
+        /// <param name="shape">The shape (k) of the Weibull distribution.</param>
+        /// <param name="scale">The scale (λ) of the Weibull distribution.</param>
         /// <returns>a sequence of samples from the distribution.</returns>
         public static IEnumerable<double> Samples(System.Random rng, double shape, double scale)
         {

src/Numerics/Distributions/Wishart.cs

@@ -55,12 +55,12 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// The degrees of freedom for the Wishart distribution.
         /// </summary>
-        double _nu;
+        double _degreeOfFreedom;
 
         /// <summary>
         /// The scale matrix for the Wishart distribution.
         /// </summary>
-        Matrix<double> _s;
+        Matrix<double> _scale;
 
         /// <summary>
         /// Caches the Cholesky factorization of the scale matrix.
@@ -70,66 +70,66 @@ namespace MathNet.Numerics.Distributions
         /// <summary>
         /// Initializes a new instance of the <see cref="Wishart"/> class. 
         /// </summary>
-        /// <param name="nu">The degrees of freedom for the Wishart distribution.</param>
-        /// <param name="s">The scale matrix for the Wishart distribution.</param>
-        public Wishart(double nu, Matrix<double> s)
+        /// <param name="degreeOfFreedom">The degrees of freedom (n) for the Wishart distribution.</param>
+        /// <param name="scale">The scale matrix (V) for the Wishart distribution.</param>
+        public Wishart(double degreeOfFreedom, Matrix<double> scale)
         {
             _random = new System.Random();
-            SetParameters(nu, s);
+            SetParameters(degreeOfFreedom, scale);
         }
 
         /// <summary>
         /// Initializes a new instance of the <see cref="Wishart"/> class. 
         /// </summary>
-        /// <param name="nu">The degrees of freedom for the Wishart distribution.</param>
-        /// <param name="s">The scale matrix for the Wishart distribution.</param>
+        /// <param name="degreeOfFreedom">The degrees of freedom (n) for the Wishart distribution.</param>
+        /// <param name="scale">The scale matrix (V) for the Wishart distribution.</param>
         /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
-        public Wishart(double nu, Matrix<double> s, System.Random randomSource)
+        public Wishart(double degreeOfFreedom, Matrix<double> scale, System.Random randomSource)
         {
             _random = randomSource ?? new System.Random();
-            SetParameters(nu, s);
+            SetParameters(degreeOfFreedom, scale);
         }
 
         /// <summary>
         /// Sets the parameters of the distribution after checking their validity.
         /// </summary>
-        /// <param name="nu">The degrees of freedom for the Wishart distribution.</param>
-        /// <param name="s">The scale matrix for the Wishart distribution.</param>
+        /// <param name="degreeOfFreedom">The degrees of freedom (n) for the Wishart distribution.</param>
+        /// <param name="scale">The scale matrix (V) for the Wishart distribution.</param>
         /// <exception cref="ArgumentOutOfRangeException">When the parameters don't pass the <see cref="IsValidParameterSet"/> function.</exception>
-        void SetParameters(double nu, Matrix<double> s)
+        void SetParameters(double degreeOfFreedom, Matrix<double> scale)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(nu, s))
+            if (Control.CheckDistributionParameters && !IsValidParameterSet(degreeOfFreedom, scale))
             {
                 throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
             }
 
-            _nu = nu;
-            _s = s;
-            _chol = Cholesky<double>.Create(_s);
+            _degreeOfFreedom = degreeOfFreedom;
+            _scale = scale;
+            _chol = Cholesky<double>.Create(_scale);
         }
 
         /// <summary>
         /// Checks whether the parameters of the distribution are valid. 
         /// </summary>
-        /// <param name="nu">The degrees of freedom for the Wishart distribution.</param>
-        /// <param name="s">The scale matrix for the Wishart distribution.</param>
+        /// <param name="degreeOfFreedom">The degrees of freedom (n) for the Wishart distribution.</param>
+        /// <param name="scale">The scale matrix (V) for the Wishart distribution.</param>
         /// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
-        static bool IsValidParameterSet(double nu, Matrix<double> s)
+        static bool IsValidParameterSet(double degreeOfFreedom, Matrix<double> scale)
         {
-            if (s.RowCount != s.ColumnCount)
+            if (scale.RowCount != scale.ColumnCount)
             {
                 return false;
             }
 
-            for (var i = 0; i < s.RowCount; i++)
+            for (var i = 0; i < scale.RowCount; i++)
             {
-                if (s.At(i, i) <= 0.0)
+                if (scale.At(i, i) <= 0.0)
                 {
                     return false;
                 }
             }
 
-            if (nu <= 0.0 || Double.IsNaN(nu))
+            if (degreeOfFreedom <= 0.0 || Double.IsNaN(degreeOfFreedom))
             {
                 return false;
             }
@@ -138,21 +138,21 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Gets or sets the degrees of freedom for the Wishart distribution.
+        /// Gets or sets the degrees of freedom (n) for the Wishart distribution.
         /// </summary>
-        public double Nu
+        public double DegreeOfFreedom
         {
-            get { return _nu; }
-            set { SetParameters(value, _s); }
+            get { return _degreeOfFreedom; }
+            set { SetParameters(value, _scale); }
         }
 
         /// <summary>
-        /// Gets or sets the scale matrix for the Wishart distribution.
+        /// Gets or sets the scale matrix (V) for the Wishart distribution.
         /// </summary>
-        public Matrix<double> S
+        public Matrix<double> Scale
         {
-            get { return _s; }
-            set { SetParameters(_nu, value); }
+            get { return _scale; }
+            set { SetParameters(_degreeOfFreedom, value); }
         }
 
         /// <summary>
@@ -161,7 +161,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a string representation of the distribution.</returns>
         public override string ToString()
         {
-            return "Wishart(Nu = " + _nu + ", Rows = " + _s.RowCount + ", Columns = " + _s.ColumnCount + ")";
+            return "Wishart(DegreeOfFreedom = " + _degreeOfFreedom + ", Rows = " + _scale.RowCount + ", Columns = " + _scale.ColumnCount + ")";
         }
 
         /// <summary>
@@ -187,7 +187,7 @@ namespace MathNet.Numerics.Distributions
         /// <value>The mean of the distribution.</value>
         public Matrix<double> Mean
         {
-            get { return _nu*_s; }
+            get { return _degreeOfFreedom*_scale; }
         }
 
         /// <summary>
@@ -196,7 +196,7 @@ namespace MathNet.Numerics.Distributions
         /// <value>The mode of the distribution.</value>
         public Matrix<double> Mode
         {
-            get { return (_nu - _s.RowCount - 1.0)*_s; }
+            get { return (_degreeOfFreedom - _scale.RowCount - 1.0)*_scale; }
         }
 
         /// <summary>
@@ -207,12 +207,12 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                var res = _s.CreateMatrix(_s.RowCount, _s.ColumnCount);
+                var res = _scale.CreateMatrix(_scale.RowCount, _scale.ColumnCount);
                 for (var i = 0; i < res.RowCount; i++)
                 {
                     for (var j = 0; j < res.ColumnCount; j++)
                     {
-                        res.At(i, j, _nu*((_s.At(i, j)*_s.At(i, j)) + (_s.At(i, i)*_s.At(j, j))));
+                        res.At(i, j, _degreeOfFreedom*((_scale.At(i, j)*_scale.At(i, j)) + (_scale.At(i, i)*_scale.At(j, j))));
                     }
                 }
 
@@ -228,11 +228,11 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the density at <paramref name="x"/>.</returns>
         public double Density(Matrix<double> x)
         {
-            var p = _s.RowCount;
+            var p = _scale.RowCount;
 
             if (x.RowCount != p || x.ColumnCount != p)
             {
-                throw Matrix.DimensionsDontMatch<ArgumentOutOfRangeException>(x, _s, "x");
+                throw Matrix.DimensionsDontMatch<ArgumentOutOfRangeException>(x, _scale, "x");
             }
 
             var dX = x.Determinant();
@@ -242,13 +242,13 @@ namespace MathNet.Numerics.Distributions
             var gp = Math.Pow(Constants.Pi, p*(p - 1.0)/4.0);
             for (var j = 1; j <= p; j++)
             {
-                gp *= SpecialFunctions.Gamma((_nu + 1.0 - j)/2.0);
+                gp *= SpecialFunctions.Gamma((_degreeOfFreedom + 1.0 - j)/2.0);
             }
 
-            return Math.Pow(dX, (_nu - p - 1.0)/2.0)
+            return Math.Pow(dX, (_degreeOfFreedom - p - 1.0)/2.0)
                    *Math.Exp(-0.5*siX.Trace())
-                   /Math.Pow(2.0, _nu*p/2.0)
-                   /Math.Pow(_chol.Determinant, _nu/2.0)
+                   /Math.Pow(2.0, _degreeOfFreedom*p/2.0)
+                   /Math.Pow(_chol.Determinant, _degreeOfFreedom/2.0)
                    /gp;
         }
 
@@ -261,7 +261,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>A random number from this distribution.</returns>
         public Matrix<double> Sample()
         {
-            return DoSample(RandomSource, _nu, _s, _chol);
+            return DoSample(RandomSource, _degreeOfFreedom, _scale, _chol);
         }
 
         /// <summary>
@@ -271,37 +271,37 @@ namespace MathNet.Numerics.Distributions
         ///     Applied Statistics, Vol. 21, No. 3 (1972), pp. 341-345
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="nu">The degrees of freedom.</param>
-        /// <param name="s">The scale matrix.</param>
+        /// <param name="degreeOfFreedom">The degrees of freedom (n) for the Wishart distribution.</param>
+        /// <param name="scale">The scale matrix (V) for the Wishart distribution.</param>
         /// <returns>a sequence of samples from the distribution.</returns>
-        public static Matrix<double> Sample(System.Random rnd, double nu, Matrix<double> s)
+        public static Matrix<double> Sample(System.Random rnd, double degreeOfFreedom, Matrix<double> scale)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(nu, s))
+            if (Control.CheckDistributionParameters && !IsValidParameterSet(degreeOfFreedom, scale))
             {
                 throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
             }
 
-            return DoSample(rnd, nu, s, Cholesky<double>.Create(s));
+            return DoSample(rnd, degreeOfFreedom, scale, Cholesky<double>.Create(scale));
         }
 
         /// <summary>
         /// Samples the distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="nu">The nu parameter to use.</param>
-        /// <param name="s">The S parameter to use.</param>
+        /// <param name="degreeOfFreedom">The degrees of freedom (n) for the Wishart distribution.</param>
+        /// <param name="scale">The scale matrix (V) for the Wishart distribution.</param>
         /// <param name="chol">The cholesky decomposition to use.</param>
         /// <returns>a random number from the distribution.</returns>
-        static Matrix<double> DoSample(System.Random rnd, double nu, Matrix<double> s, Cholesky<double> chol)
+        static Matrix<double> DoSample(System.Random rnd, double degreeOfFreedom, Matrix<double> scale, Cholesky<double> chol)
         {
-            var count = s.RowCount;
+            var count = scale.RowCount;
 
             // First generate a lower triangular matrix with Sqrt(Chi-Squares) on the diagonal
             // and normal distributed variables in the lower triangle.
             var a = new DenseMatrix(count, count);
             for (var d = 0; d < count; d++)
             {
-                a.At(d, d, Math.Sqrt(Gamma.Sample(rnd, (nu - d)/2.0, 0.5)));
+                a.At(d, d, Math.Sqrt(Gamma.Sample(rnd, (degreeOfFreedom - d)/2.0, 0.5)));
             }
 
             for (var i = 1; i < count; i++)

src/Numerics/Distributions/Zipf.cs

@@ -120,15 +120,6 @@ namespace MathNet.Numerics.Distributions
             _n = n;
         }
 
-        /// <summary>
-        /// Gets or sets the random number generator which is used to draw random samples.
-        /// </summary>
-        public System.Random RandomSource
-        {
-            get { return _random; }
-            set { _random = value ?? new System.Random(); }
-        }
-
         /// <summary>
         /// Gets or sets the s parameter of the distribution.
         /// </summary>
@@ -147,6 +138,15 @@ namespace MathNet.Numerics.Distributions
             set { SetParameters(_s, value); }
         }
 
+        /// <summary>
+        /// Gets or sets the random number generator which is used to draw random samples.
+        /// </summary>
+        public System.Random RandomSource
+        {
+            get { return _random; }
+            set { _random = value ?? new System.Random(); }
+        }
+
         /// <summary>
         /// Gets the mean of the distribution.
         /// </summary>

src/UnitTests/DistributionTests/Continuous/BetaTests.cs

@@ -1,4 +1,4 @@
-// <copyright file="BetaTests.cs" company="Math.NET">
+// <copyright file="BetaTests.cs" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
@@ -90,8 +90,8 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         [Test]
         public void ValidateToString()
         {
-            var n = new Beta(1.0, 2.0);
-            Assert.AreEqual("Beta(A = 1, B = 2)", n.ToString());
+            var n = new Beta(1d, 2d);
+            Assert.AreEqual("Beta(α = 1, β = 2)", n.ToString());
         }
 
         /// <summary>

src/UnitTests/DistributionTests/Continuous/CauchyTests.cs

@@ -1,4 +1,4 @@
-// <copyright file="CauchyTests.cs" company="Math.NET">
+// <copyright file="CauchyTests.cs" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
@@ -95,8 +95,8 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         [Test]
         public void ValidateToString()
         {
-            var n = new Cauchy(1.0, 2.0);
-            Assert.AreEqual("Cauchy(Location = 1, Scale = 2)", n.ToString());
+            var n = new Cauchy(1d, 2d);
+            Assert.AreEqual("Cauchy(x0 = 1, γ = 2)", n.ToString());
         }
 
         /// <summary>

src/UnitTests/DistributionTests/Continuous/ContinuousUniformTests.cs

@@ -55,8 +55,8 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         public void CanCreateContinuousUniform()
         {
             var n = new ContinuousUniform();
-            Assert.AreEqual(0.0, n.Lower);
-            Assert.AreEqual(1.0, n.Upper);
+            Assert.AreEqual(0.0, n.LowerBound);
+            Assert.AreEqual(1.0, n.UpperBound);
         }
 
         /// <summary>
@@ -74,8 +74,8 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         public void CanCreateContinuousUniform(double lower, double upper)
         {
             var n = new ContinuousUniform(lower, upper);
-            Assert.AreEqual(lower, n.Lower);
-            Assert.AreEqual(upper, n.Upper);
+            Assert.AreEqual(lower, n.LowerBound);
+            Assert.AreEqual(upper, n.UpperBound);
         }
 
         /// <summary>
@@ -115,7 +115,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         {
             new ContinuousUniform
             {
-                Lower = lower
+                LowerBound = lower
             };
         }
 
@@ -126,7 +126,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         public void SetBadLowerFails()
         {
             var n = new ContinuousUniform();
-            Assert.Throws<ArgumentOutOfRangeException>(() => n.Lower = 3.0);
+            Assert.Throws<ArgumentOutOfRangeException>(() => n.LowerBound = 3.0);
         }
 
         /// <summary>
@@ -140,7 +140,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         {
             new ContinuousUniform
             {
-                Upper = upper
+                UpperBound = upper
             };
         }
 
@@ -151,7 +151,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         public void SetBadUpperFails()
         {
             var n = new ContinuousUniform();
-            Assert.Throws<ArgumentOutOfRangeException>(() => n.Upper = -1.0);
+            Assert.Throws<ArgumentOutOfRangeException>(() => n.UpperBound = -1.0);
         }
 
         /// <summary>

src/UnitTests/DistributionTests/Continuous/ErlangTests.cs

@@ -1,4 +1,4 @@
-// <copyright file="ErlangTests.cs" company="Math.NET">
+// <copyright file="ErlangTests.cs" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
@@ -61,7 +61,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         {
             var n = new Erlang(shape, invScale);
             Assert.AreEqual(shape, n.Shape);
-            Assert.AreEqual(invScale, n.InvScale);
+            Assert.AreEqual(invScale, n.Rate);
         }
 
         /// <summary>
@@ -92,9 +92,9 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         [TestCase(10, Double.PositiveInfinity)]
         public void CanCreateErlangWithShapeInvScale(int shape, double invScale)
         {
-            var n = Erlang.WithShapeInvScale(shape, invScale);
+            var n = Erlang.WithShapeRate(shape, invScale);
             Assert.AreEqual(shape, n.Shape);
-            Assert.AreEqual(invScale, n.InvScale);
+            Assert.AreEqual(invScale, n.Rate);
         }
 
         /// <summary>
@@ -121,8 +121,8 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         [Test]
         public void ValidateToString()
         {
-            var n = new Erlang(1, 2.0);
-            Assert.AreEqual("Erlang(Shape = 1, Inverse Scale = 2)", n.ToString());
+            var n = new Erlang(1, 2d);
+            Assert.AreEqual("Erlang(Shape = 1, λ = 2)", n.ToString());
         }
 
         /// <summary>
@@ -193,7 +193,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         {
             new Erlang(1, 1.0)
             {
-                InvScale = invScale
+                Rate = invScale
             };
         }
 
@@ -204,7 +204,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         public void SetInvScaleFailsWithNegativeInvScale()
         {
             var n = new Erlang(1, 1.0);
-            Assert.Throws<ArgumentOutOfRangeException>(() => n.InvScale = -1.0);
+            Assert.Throws<ArgumentOutOfRangeException>(() => n.Rate = -1.0);
         }
 
         /// <summary>

src/UnitTests/DistributionTests/Continuous/ExponentialTests.cs

@@ -1,4 +1,4 @@
-// <copyright file="ExponentialTests.cs" company="Math.NET">
+// <copyright file="ExponentialTests.cs" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
@@ -58,7 +58,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         public void CanCreateExponential(double lambda)
         {
             var n = new Exponential(lambda);
-            Assert.AreEqual(lambda, n.Lambda);
+            Assert.AreEqual(lambda, n.Rate);
         }
 
         /// <summary>
@@ -79,8 +79,8 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         [Test]
         public void ValidateToString()
         {
-            var n = new Exponential(2.0);
-            Assert.AreEqual("Exponential(Lambda = 2)", n.ToString());
+            var n = new Exponential(2d);
+            Assert.AreEqual("Exponential(λ = 2)", n.ToString());
         }
 
         /// <summary>
@@ -97,7 +97,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         {
             new Exponential(1.0)
             {
-                Lambda = lambda
+                Rate = lambda
             };
         }
 
@@ -108,7 +108,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         public void SetLambdaFailsWithNegativeLambda()
         {
             var n = new Exponential(1.0);
-            Assert.Throws<ArgumentOutOfRangeException>(() => n.Lambda = -1.0);
+            Assert.Throws<ArgumentOutOfRangeException>(() => n.Rate = -1.0);
         }
 
         /// <summary>

src/UnitTests/DistributionTests/Continuous/GammaTests.cs

@@ -1,4 +1,4 @@
-// <copyright file="GammaTests.cs" company="Math.NET">
+// <copyright file="GammaTests.cs" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
@@ -63,7 +63,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         {
             var n = new Gamma(shape, invScale);
             Assert.AreEqual(shape, n.Shape);
-            Assert.AreEqual(invScale, n.InvScale);
+            Assert.AreEqual(invScale, n.Rate);
         }
 
         /// <summary>
@@ -94,9 +94,9 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         [TestCase(10.0, Double.PositiveInfinity)]
         public void CanCreateGammaWithShapeInvScale(double shape, double invScale)
         {
-            var n = Gamma.WithShapeInvScale(shape, invScale);
+            var n = Gamma.WithShapeRate(shape, invScale);
             Assert.AreEqual(shape, n.Shape);
-            Assert.AreEqual(invScale, n.InvScale);
+            Assert.AreEqual(invScale, n.Rate);
         }
 
         /// <summary>
@@ -123,8 +123,8 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         [Test]
         public void ValidateToString()
         {
-            var n = new Gamma(1.0, 2.0);
-            Assert.AreEqual("Gamma(Shape = 1, Inverse Scale = 2)", n.ToString());
+            var n = new Gamma(1d, 2d);
+            Assert.AreEqual("Gamma(α = 1, β = 2)", n.ToString());
         }
 
         /// <summary>
@@ -197,7 +197,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         {
             new Gamma(1.0, 1.0)
             {
-                InvScale = invScale
+                Rate = invScale
             };
         }
 
@@ -208,7 +208,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         public void SetInvScaleFailsWithNegativeInvScale()
         {
             var n = new Gamma(1.0, 1.0);
-            Assert.Throws<ArgumentOutOfRangeException>(() => n.InvScale = -1.0);
+            Assert.Throws<ArgumentOutOfRangeException>(() => n.Rate = -1.0);
         }
 
         /// <summary>

src/UnitTests/DistributionTests/Continuous/InverseGammaTests.cs

@@ -1,4 +1,4 @@
-// <copyright file="InverseGammaTests.cs" company="Math.NET">
+// <copyright file="InverseGammaTests.cs" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
@@ -87,8 +87,8 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         [Test]
         public void ValidateToString()
         {
-            var n = new InverseGamma(1.1, 2.1);
-            Assert.AreEqual(String.Format("InverseGamma(Shape = {0}, Inverse Scale = {1})", n.Shape, n.Scale), n.ToString());
+            var n = new InverseGamma(1.1d, 2.1d);
+            Assert.AreEqual("InverseGamma(α = 1.1, β = 2.1)", n.ToString());
         }
 
         /// <summary>

src/UnitTests/DistributionTests/Continuous/LaplaceTests.cs

@@ -1,4 +1,4 @@
-// <copyright file="LaplaceTests.cs" company="Math.NET">
+// <copyright file="LaplaceTests.cs" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
@@ -81,8 +81,8 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         [Test]
         public void ValidateToString()
         {
-            var n = new Laplace(-1.0, 2.0);
-            Assert.AreEqual("Laplace(Location = -1, Scale = 2)", n.ToString());
+            var n = new Laplace(-1d, 2d);
+            Assert.AreEqual("Laplace(μ = -1, b = 2)", n.ToString());
         }
 
         /// <summary>

src/UnitTests/DistributionTests/Continuous/LogNormalTests.cs

@@ -1,4 +1,4 @@
-// <copyright file="LogNormalTests.cs" company="Math.NET">
+// <copyright file="LogNormalTests.cs" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
@@ -86,8 +86,8 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         [Test]
         public void ValidateToString()
         {
-            var n = new LogNormal(1.0, 2.0);
-            Assert.AreEqual("LogNormal(Mu = 1, Sigma = 2)", n.ToString());
+            var n = new LogNormal(1d, 2d);
+            Assert.AreEqual("LogNormal(μ = 1, σ = 2)", n.ToString());
         }
 
         /// <summary>

src/UnitTests/DistributionTests/Continuous/NormalTests.cs

@@ -1,4 +1,4 @@
-// <copyright file="NormalTests.cs" company="Math.NET">
+// <copyright file="NormalTests.cs" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
@@ -151,8 +151,8 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         [Test]
         public void ValidateToString()
         {
-            var n = new Normal(1.0, 2.0);
-            Assert.AreEqual("Normal(Mean = 1, StdDev = 2)", n.ToString());
+            var n = new Normal(1d, 2d);
+            Assert.AreEqual("Normal(μ = 1, σ = 2)", n.ToString());
         }
 
         /// <summary>

src/UnitTests/DistributionTests/Continuous/ParetoTests.cs

@@ -1,4 +1,4 @@
-// <copyright file="ParetoTests.cs" company="Math.NET">
+// <copyright file="ParetoTests.cs" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
@@ -87,8 +87,8 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         [Test]
         public void ValidateToString()
         {
-            var n = new Pareto(1.0, 2.0);
-            Assert.AreEqual("Pareto(Scale = 1, Shape = 2)", n.ToString());
+            var n = new Pareto(1d, 2d);
+            Assert.AreEqual("Pareto(xm = 1, α = 2)", n.ToString());
         }
 
         /// <summary>

src/UnitTests/DistributionTests/Continuous/RayleighTests.cs

@@ -1,4 +1,4 @@
-// <copyright file="RayleighTests.cs" company="Math.NET">
+// <copyright file="RayleighTests.cs" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
@@ -79,8 +79,8 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         [Test]
         public void ValidateToString()
         {
-            var n = new Rayleigh(2.0);
-            Assert.AreEqual("Rayleigh(Scale = 2)", n.ToString());
+            var n = new Rayleigh(2d);
+            Assert.AreEqual("Rayleigh(σ = 2)", n.ToString());
         }
 
         /// <summary>

src/UnitTests/DistributionTests/Continuous/StableTests.cs

@@ -1,4 +1,4 @@
-// <copyright file="StableTests.cs" company="Math.NET">
+// <copyright file="StableTests.cs" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
@@ -103,8 +103,8 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         [Test]
         public void ValidateToString()
         {
-            var n = new Stable(1.2, 0.3, 1.0, 2.0);
-            Assert.AreEqual(String.Format("Stable(Stability = {0}, Skewness = {1}, Scale = {2}, Location = {3})", n.Alpha, n.Beta, n.Scale, n.Location), n.ToString());
+            var n = new Stable(1.2d, 0.3d, 1d, 2d);
+            Assert.AreEqual("Stable(α = 1.2, β = 0.3, c = 1, μ = 2)", n.ToString());
         }
 
         /// <summary>

src/UnitTests/DistributionTests/Continuous/WeibullTests.cs

@@ -1,4 +1,4 @@
-// <copyright file="WeibullTests.cs" company="Math.NET">
+// <copyright file="WeibullTests.cs" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
@@ -89,8 +89,8 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
         [Test]
         public void ValidateToString()
         {
-            var n = new Weibull(1.0, 2.0);
-            Assert.AreEqual("Weibull(Shape = 1, Scale = 2)", n.ToString());
+            var n = new Weibull(1d, 2d);
+            Assert.AreEqual("Weibull(k = 1, λ = 2)", n.ToString());
         }
 
         /// <summary>

src/UnitTests/DistributionTests/Discrete/ConwayMaxwellPoissonTests.cs

@@ -1,4 +1,4 @@
-// <copyright file="ConwayMaxwellPoissonTests.cs" company="Math.NET">
+// <copyright file="ConwayMaxwellPoissonTests.cs" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
@@ -50,7 +50,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Discrete
         /// Can create <c>ConwayMaxwellPoisson</c>.
         /// </summary>
         /// <param name="lambda">Lambda value.</param>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         [TestCase(0.1, 0.0)]
         [TestCase(1.0, 2.5)]
         [TestCase(2.5, 3.0)]
@@ -78,8 +78,8 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Discrete
         [Test]
         public void ValidateToString()
         {
-            var d = new ConwayMaxwellPoisson(1.0, 2.0);
-            Assert.AreEqual("ConwayMaxwellPoisson(Lambda = 1, Nu = 2)", d.ToString());
+            var d = new ConwayMaxwellPoisson(1d, 2d);
+            Assert.AreEqual("ConwayMaxwellPoisson(λ = 1, ν = 2)", d.ToString());
         }
 
         /// <summary>
@@ -99,9 +99,9 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Discrete
         }
 
         /// <summary>
-        /// Can set Nu.
+        /// Can set DegreeOfFreedom.
         /// </summary>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         [TestCase(0.0)]
         [TestCase(3.0)]
         [TestCase(10.0)]
@@ -129,9 +129,9 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Discrete
         }
 
         /// <summary>
-        /// Set Nu with bad values fails.
+        /// Set DegreeOfFreedom with bad values fails.
         /// </summary>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         [TestCase(-0.1)]
         [TestCase(-1.0)]
         [TestCase(-10.0)]
@@ -186,7 +186,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Discrete
         /// Validate mean.
         /// </summary>
         /// <param name="lambda">Lambda value.</param>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         /// <param name="mean">Expected value.</param>
         [TestCase(1, 1, 1.0)]
         [TestCase(2, 1, 2.0)]
@@ -224,7 +224,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Discrete
         /// Validate probability.
         /// </summary>
         /// <param name="lambda">Lambda value.</param>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         /// <param name="x">Input X value.</param>
         /// <param name="p">Expected value.</param>
         [TestCase(1.0, 1.0, 1, 0.367879441171442)]
@@ -243,7 +243,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Discrete
         /// Validate probability log.
         /// </summary>
         /// <param name="lambda">Lambda value.</param>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         /// <param name="x">Input X value.</param>
         /// <param name="pln">Expected value.</param>
         [TestCase(1.0, 1.0, 1, -1.0)]
@@ -283,7 +283,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Discrete
         /// Validate cumulative distribution.
         /// </summary>
         /// <param name="lambda">Lambda value.</param>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         /// <param name="x">Input X value.</param>
         /// <param name="cdf">Expected value.</param>
         [TestCase(1.0, 1.0, 1, 0.735758882342885)]

src/UnitTests/DistributionTests/Multivariate/InverseWishartTests.cs

@@ -1,4 +1,4 @@
-// <copyright file="InverseWishartTests.cs" company="Math.NET">
+// <copyright file="InverseWishartTests.cs" company="Math.NET">
 // Math.NET Numerics, part of the Math.NET Project
 // http://numerics.mathdotnet.com
 // http://github.com/mathnet/mathnet-numerics
@@ -50,7 +50,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
         /// <summary>
         /// Can create inverse Wishart.
         /// </summary>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         /// <param name="order">Scale matrix order.</param>
         [TestCase(0.1, 2)]
         [TestCase(1.0, 5)]
@@ -60,12 +60,12 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
             var matrix = MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(order);
             var d = new InverseWishart(nu, matrix);
 
-            Assert.AreEqual(nu, d.Nu);
-            for (var i = 0; i < d.S.RowCount; i++)
+            Assert.AreEqual(nu, d.DegreeOfFreedom);
+            for (var i = 0; i < d.Scale.RowCount; i++)
             {
-                for (var j = 0; j < d.S.ColumnCount; j++)
+                for (var j = 0; j < d.Scale.ColumnCount; j++)
                 {
-                    Assert.AreEqual(matrix[i, j], d.S[i, j]);
+                    Assert.AreEqual(matrix[i, j], d.Scale[i, j]);
                 }
             }
         }
@@ -73,7 +73,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
         /// <summary>
         /// Fail create inverse Wishart with bad parameters.
         /// </summary>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         /// <param name="order">Scale matrix order.</param>
         [TestCase(0.1, 2)]
         [TestCase(1.0, 5)]
@@ -89,7 +89,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
         /// <summary>
         /// Fail create inverse Wishart with bad parameters.
         /// </summary>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         /// <param name="order">Scale matrix order.</param>
         [TestCase(-1.0, 2)]
         [TestCase(Double.NaN, 5)]
@@ -135,8 +135,8 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
         [Test]
         public void ValidateToString()
         {
-            var d = new InverseWishart(1.0, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(2));
-            Assert.AreEqual("InverseWishart(Nu = 1, Rows = 2, Columns = 2)", d.ToString());
+            var d = new InverseWishart(1d, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(2));
+            Assert.AreEqual("InverseWishart(ν = 1, Rows = 2, Columns = 2)", d.ToString());
         }
 
         /// <summary>
@@ -149,13 +149,13 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
         public void CanGetNu(double nu)
         {
             var d = new InverseWishart(nu, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(2));
-            Assert.AreEqual(nu, d.Nu);
+            Assert.AreEqual(nu, d.DegreeOfFreedom);
         }
 
         /// <summary>
-        /// Can set Nu.
+        /// Can set DegreeOfFreedom.
         /// </summary>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         [TestCase(1.0)]
         [TestCase(2.0)]
         [TestCase(5.0)]
@@ -163,7 +163,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
         {
             new InverseWishart(1.0, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(2))
             {
-                Nu = nu
+                DegreeOfFreedom = nu
             };
         }
 
@@ -181,7 +181,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
             {
                 for (var j = 0; j < Order; j++)
                 {
-                    Assert.AreEqual(matrix[i, j], d.S[i, j]);
+                    Assert.AreEqual(matrix[i, j], d.Scale[i, j]);
                 }
             }
         }
@@ -194,14 +194,14 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
         {
             new InverseWishart(1.0, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(2))
             {
-                S = MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(2)
+                Scale = MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(2)
             };
         }
 
         /// <summary>
         /// Validate mean.
         /// </summary>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         /// <param name="order">Scale matrix order.</param>
         [TestCase(0.1, 2)]
         [TestCase(1.0, 5)]
@@ -211,11 +211,11 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
             var d = new InverseWishart(nu, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(order));
 
             var mean = d.Mean;
-            for (var i = 0; i < d.S.RowCount; i++)
+            for (var i = 0; i < d.Scale.RowCount; i++)
             {
-                for (var j = 0; j < d.S.ColumnCount; j++)
+                for (var j = 0; j < d.Scale.ColumnCount; j++)
                 {
-                    Assert.AreEqual(d.S[i, j] * (1.0 / (nu - d.S.RowCount - 1.0)), mean[i, j]);
+                    Assert.AreEqual(d.Scale[i, j] * (1.0 / (nu - d.Scale.RowCount - 1.0)), mean[i, j]);
                 }
             }
         }
@@ -223,7 +223,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
         /// <summary>
         /// Validate mode.
         /// </summary>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         /// <param name="order">Scale matrix order.</param>
         [TestCase(0.1, 2)]
         [TestCase(1.0, 5)]
@@ -233,11 +233,11 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
             var d = new InverseWishart(nu, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(order));
 
             var mode = d.Mode;
-            for (var i = 0; i < d.S.RowCount; i++)
+            for (var i = 0; i < d.Scale.RowCount; i++)
             {
-                for (var j = 0; j < d.S.ColumnCount; j++)
+                for (var j = 0; j < d.Scale.ColumnCount; j++)
                 {
-                    Assert.AreEqual(d.S[i, j] * (1.0 / (nu + d.S.RowCount + 1.0)), mode[i, j]);
+                    Assert.AreEqual(d.Scale[i, j] * (1.0 / (nu + d.Scale.RowCount + 1.0)), mode[i, j]);
                 }
             }
         }
@@ -245,7 +245,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
         /// <summary>
         /// Validate variance.
         /// </summary>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         /// <param name="order">Scale matrix order.</param>
         [TestCase(0.1, 2)]
         [TestCase(1.0, 5)]
@@ -255,12 +255,12 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
             var d = new InverseWishart(nu, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(order));
 
             var variance = d.Variance;
-            for (var i = 0; i < d.S.RowCount; i++)
+            for (var i = 0; i < d.Scale.RowCount; i++)
             {
-                for (var j = 0; j < d.S.ColumnCount; j++)
+                for (var j = 0; j < d.Scale.ColumnCount; j++)
                 {
-                    var num1 = ((nu - d.S.RowCount + 1) * d.S[i, j] * d.S[i, j]) + ((nu - d.S.RowCount - 1) * d.S[i, i] * d.S[j, j]);
-                    var num2 = (nu - d.S.RowCount) * (nu - d.S.RowCount - 1) * (nu - d.S.RowCount - 1) * (nu - d.S.RowCount - 3);
+                    var num1 = ((nu - d.Scale.RowCount + 1) * d.Scale[i, j] * d.Scale[i, j]) + ((nu - d.Scale.RowCount - 1) * d.Scale[i, i] * d.Scale[j, j]);
+                    var num2 = (nu - d.Scale.RowCount) * (nu - d.Scale.RowCount - 1) * (nu - d.Scale.RowCount - 1) * (nu - d.Scale.RowCount - 3);
                     Assert.AreEqual(num1 / num2, variance[i, j]);
                 }
             }
@@ -269,7 +269,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
         /// <summary>
         /// Validate density.
         /// </summary>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         /// <param name="density">Expected value.</param>
         [TestCase(1.0, 0.03228684517430723)]
         [TestCase(2.0, 0.018096748360719193)]

src/UnitTests/DistributionTests/Multivariate/NormalGammaTests.cs

@@ -264,7 +264,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
             var ng = new NormalGamma(meanLocation, meanScale, precShape, precInvScale);
             var pm = ng.PrecisionMarginal();
             Assert.AreEqual(precShape, pm.Shape);
-            Assert.AreEqual(precInvScale, pm.InvScale);
+            Assert.AreEqual(precInvScale, pm.Rate);
         }
 
         /// <summary>

src/UnitTests/DistributionTests/Multivariate/WishartTests.cs

@@ -50,7 +50,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
         /// <summary>
         /// Can create wishart.
         /// </summary>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         /// <param name="order">Scale matrix order.</param>
         [TestCase(0.1, 2)]
         [TestCase(1.0, 5)]
@@ -61,12 +61,12 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
 
             var d = new Wishart(nu, matrix);
 
-            Assert.AreEqual(nu, d.Nu);
-            for (var i = 0; i < d.S.RowCount; i++)
+            Assert.AreEqual(nu, d.DegreeOfFreedom);
+            for (var i = 0; i < d.Scale.RowCount; i++)
             {
-                for (var j = 0; j < d.S.ColumnCount; j++)
+                for (var j = 0; j < d.Scale.ColumnCount; j++)
                 {
-                    Assert.AreEqual(matrix[i, j], d.S[i, j]);
+                    Assert.AreEqual(matrix[i, j], d.Scale[i, j]);
                 }
             }
         }
@@ -74,7 +74,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
         /// <summary>
         /// Fail create Wishart with bad parameters.
         /// </summary>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         /// <param name="order">Scale matrix order.</param>
         [TestCase(0.0, 2)]
         [TestCase(0.1, 5)]
@@ -91,7 +91,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
         /// <summary>
         /// Fail create Wishart with bad parameters.
         /// </summary>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         /// <param name="order">Scale matrix order.</param>
         [TestCase(-1.0, 2)]
         [TestCase(Double.NaN, 5)]
@@ -140,26 +140,26 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
         public void ValidateToString()
         {
             var d = new Wishart(1.0, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(2));
-            Assert.AreEqual("Wishart(Nu = 1, Rows = 2, Columns = 2)", d.ToString());
+            Assert.AreEqual("Wishart(DegreeOfFreedom = 1, Rows = 2, Columns = 2)", d.ToString());
         }
 
         /// <summary>
-        /// Can get Nu.
+        /// Can get DegreeOfFreedom.
         /// </summary>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         [TestCase(1.0)]
         [TestCase(2.0)]
         [TestCase(5.0)]
         public void CanGetNu(double nu)
         {
             var d = new Wishart(nu, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(2));
-            Assert.AreEqual(nu, d.Nu);
+            Assert.AreEqual(nu, d.DegreeOfFreedom);
         }
 
         /// <summary>
-        /// Can set Nu.
+        /// Can set DegreeOfFreedom.
         /// </summary>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         [TestCase(1.0)]
         [TestCase(2.0)]
         [TestCase(5.0)]
@@ -167,7 +167,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
         {
             new Wishart(1.0, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(2))
             {
-                Nu = nu
+                DegreeOfFreedom = nu
             };
         }
 
@@ -185,7 +185,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
             {
                 for (var j = 0; j < Order; j++)
                 {
-                    Assert.AreEqual(matrix[i, j], d.S[i, j]);
+                    Assert.AreEqual(matrix[i, j], d.Scale[i, j]);
                 }
             }
         }
@@ -198,14 +198,14 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
         {
             new Wishart(1.0, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(2))
             {
-                S = MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(2)
+                Scale = MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(2)
             };
         }
 
         /// <summary>
         /// Validate mean.
         /// </summary>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         /// <param name="order">Scale matrix order.</param>
         [TestCase(0.1, 2)]
         [TestCase(1.0, 5)]
@@ -215,11 +215,11 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
             var d = new Wishart(nu, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(order));
 
             var mean = d.Mean;
-            for (var i = 0; i < d.S.RowCount; i++)
+            for (var i = 0; i < d.Scale.RowCount; i++)
             {
-                for (var j = 0; j < d.S.ColumnCount; j++)
+                for (var j = 0; j < d.Scale.ColumnCount; j++)
                 {
-                    Assert.AreEqual(nu * d.S[i, j], mean[i, j]);
+                    Assert.AreEqual(nu * d.Scale[i, j], mean[i, j]);
                 }
             }
         }
@@ -227,7 +227,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
         /// <summary>
         /// Validate mode.
         /// </summary>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         /// <param name="order">Scale matrix order.</param>
         [TestCase(0.1, 2)]
         [TestCase(1.0, 5)]
@@ -237,11 +237,11 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
             var d = new Wishart(nu, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(order));
 
             var mode = d.Mode;
-            for (var i = 0; i < d.S.RowCount; i++)
+            for (var i = 0; i < d.Scale.RowCount; i++)
             {
-                for (var j = 0; j < d.S.ColumnCount; j++)
+                for (var j = 0; j < d.Scale.ColumnCount; j++)
                 {
-                    Assert.AreEqual((nu - d.S.RowCount - 1.0) * d.S[i, j], mode[i, j]);
+                    Assert.AreEqual((nu - d.Scale.RowCount - 1.0) * d.Scale[i, j], mode[i, j]);
                 }
             }
         }
@@ -249,7 +249,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
         /// <summary>
         /// Validate variance.
         /// </summary>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         /// <param name="order">Scale matrix order.</param>
         [TestCase(0.1, 2)]
         [TestCase(1.0, 5)]
@@ -259,11 +259,11 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
             var d = new Wishart(nu, MatrixLoader.GenerateRandomPositiveDefiniteDenseMatrix(order));
 
             var variance = d.Variance;
-            for (var i = 0; i < d.S.RowCount; i++)
+            for (var i = 0; i < d.Scale.RowCount; i++)
             {
-                for (var j = 0; j < d.S.ColumnCount; j++)
+                for (var j = 0; j < d.Scale.ColumnCount; j++)
                 {
-                    Assert.AreEqual(nu * ((d.S[i, j] * d.S[i, j]) + (d.S[i, i] * d.S[j, j])), variance[i, j]);
+                    Assert.AreEqual(nu * ((d.Scale[i, j] * d.Scale[i, j]) + (d.Scale[i, i] * d.Scale[j, j])), variance[i, j]);
                 }
             }
         }
@@ -271,7 +271,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
         /// <summary>
         /// Validate density.
         /// </summary>
-        /// <param name="nu">Nu parameter.</param>
+        /// <param name="nu">DegreeOfFreedom parameter.</param>
         /// <param name="density">Expected value.</param>
         [TestCase(1.0, 0.014644982561926487)]
         [TestCase(2.0, 0.041042499311949421)]