Distributions: static PDF/CDF functions for StudentT, Stable, Weibull #188

src/Numerics/Distributions/Stable.cs

@@ -37,10 +37,10 @@ namespace MathNet.Numerics.Distributions
 {
     /// <summary>
     /// Continuous Univariate Stable distribution.
-    /// A random variable is said to be stable (or to have a stable distribution) if it has 
-    /// the property that a linear combination of two independent copies of the variable has 
+    /// A random variable is said to be stable (or to have a stable distribution) if it has
+    /// the property that a linear combination of two independent copies of the variable has
     /// the same distribution, up to location and scale parameters.
-    /// For details about this distribution, see 
+    /// For details about this distribution, see
     /// <a href="http://en.wikipedia.org/wiki/Stable_distribution">Wikipedia - Stable distribution</a>.
     /// </summary>
     /// <remarks><para>The distribution will use the <see cref="System.Random"/> by default.`
@@ -58,7 +58,7 @@ namespace MathNet.Numerics.Distributions
         double _location;
 
         /// <summary>
-        /// Initializes a new instance of the <see cref="Stable"/> class. 
+        /// Initializes a new instance of the <see cref="Stable"/> class.
         /// </summary>
         /// <param name="alpha">The stability (α) of the distribution. Range: 2 ≥ α > 0.</param>
         /// <param name="beta">The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.</param>
@@ -71,7 +71,7 @@ namespace MathNet.Numerics.Distributions
         }
 
         /// <summary>
-        /// Initializes a new instance of the <see cref="Stable"/> class. 
+        /// Initializes a new instance of the <see cref="Stable"/> class.
         /// </summary>
         /// <param name="alpha">The stability (α) of the distribution. Range: 2 ≥ α > 0.</param>
         /// <param name="beta">The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.</param>
@@ -93,19 +93,6 @@ namespace MathNet.Numerics.Distributions
             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 (α) of the distribution. Range: 2 ≥ α > 0.</param>
-        /// <param name="beta">The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.</param>
-        /// <param name="scale">The scale (c) of the distribution. Range: c > 0.</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)
-        {
-            return alpha > 0.0 && alpha <= 2.0 && beta >= -1.0 && beta <= 1.0 && scale > 0.0 && !Double.IsNaN(location);
-        }
-
         /// <summary>
         /// Sets the parameters of the distribution after checking their validity.
         /// </summary>
@@ -116,7 +103,8 @@ namespace MathNet.Numerics.Distributions
         /// <exception cref="ArgumentOutOfRangeException">When the parameters are out of range.</exception>
         void SetParameters(double alpha, double beta, double scale, double location)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(alpha, beta, scale, location))
+            if (alpha <= 0.0 || alpha > 2.0 || beta < -1.0 || beta > 1.0 || scale <= 0.0
+                || Double.IsNaN(alpha) || Double.IsNaN(beta) || Double.IsNaN(scale) || Double.IsNaN(location))
             {
                 throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
             }
@@ -179,7 +167,7 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                if (_alpha <= 1)
+                if (_alpha <= 1d)
                 {
                     throw new NotSupportedException();
                 }
@@ -195,7 +183,7 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                if (_alpha == 2)
+                if (_alpha == 2d)
                 {
                     return 2.0*_scale*_scale;
                 }
@@ -211,7 +199,7 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                if (_alpha == 2)
+                if (_alpha == 2d)
                 {
                     return Constants.Sqrt2*_scale;
                 }
@@ -237,7 +225,7 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                if (_alpha != 2)
+                if (_alpha != 2d)
                 {
                     throw new NotSupportedException();
                 }
@@ -254,7 +242,7 @@ namespace MathNet.Numerics.Distributions
         {
             get
             {
-                if (_beta != 0)
+                if (_beta != 0d)
                 {
                     throw new NotSupportedException();
                 }
@@ -311,40 +299,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the density at <paramref name="x"/>.</returns>
         public double Density(double x)
         {
-            if (_alpha == 2)
-            {
-                return (new Normal(_location, StdDev)).Density(x);
-            }
-
-            if (_alpha == 1 && _beta == 0)
-            {
-                return (new Cauchy(_location, _scale)).Density(x);
-            }
-
-            if (_alpha == 0.5 && _beta == 1)
-            {
-                return LevyDensity(_scale, _location, x);
-            }
-
-            throw new NotSupportedException();
-        }
-
-        /// <summary>
-        /// Computes the density of the Levy distribution.
-        /// </summary>
-        /// <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)
-        {
-            // The parameters scale and location must be correct
-            if (x < location)
-            {
-                throw new NotSupportedException();
-            }
-
-            return (Math.Sqrt(scale/Constants.Pi2)*Math.Exp(-scale/(2*(x - location))))/Math.Pow(x - location, 1.5);
+            return PDF(_alpha, _beta, _scale, _location, x);
         }
 
         /// <summary>
@@ -354,7 +309,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the log density at <paramref name="x"/>.</returns>
         public double DensityLn(double x)
         {
-            return Math.Log(Density(x));
+            return PDFLn(_alpha, _beta, _scale, _location, x);
         }
 
         /// <summary>
@@ -365,35 +320,7 @@ namespace MathNet.Numerics.Distributions
         /// <remarks>Throws a not supported exception if <c>Alpha != 2</c>, <c>(Alpha != 1 and Beta !=0)</c>, or <c>(Alpha != 0.5 and Beta != 1)</c></remarks>
         public double CumulativeDistribution(double x)
         {
-            if (_alpha == 2)
-            {
-                return (new Normal(_location, StdDev)).CumulativeDistribution(x);
-            }
-
-            if (_alpha == 1 && _beta == 0)
-            {
-                return (new Cauchy(_location, _scale)).CumulativeDistribution(x);
-            }
-
-            if (_alpha == 0.5 && _beta == 1)
-            {
-                return LevyCumulativeDistribution(_scale, _location, x);
-            }
-
-            throw new NotSupportedException();
-        }
-
-        /// <summary>
-        /// Computes the cumulative distribution function of the Levy distribution.
-        /// </summary>
-        /// <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)
-        {
-            // The parameters scale and location must be correct
-            return SpecialFunctions.Erfc(Math.Sqrt(scale/(2*(x - location))));
+            return CDF(_alpha, _beta, _scale, _location, x);
         }
 
         /// <summary>
@@ -453,6 +380,83 @@ namespace MathNet.Numerics.Distributions
             }
         }
 
+        /// <summary>
+        /// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
+        /// </summary>
+        /// <param name="alpha">The stability (α) of the distribution. Range: 2 ≥ α > 0.</param>
+        /// <param name="beta">The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.</param>
+        /// <param name="scale">The scale (c) of the distribution. Range: c > 0.</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>
+        /// <seealso cref="Density"/>
+        public static double PDF(double alpha, double beta, double scale, double location, double x)
+        {
+            if (alpha <= 0.0 || alpha > 2.0 || beta < -1.0 || beta > 1.0 || scale <= 0.0)
+                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
+
+            if (alpha == 2d) return Normal.PDF(location, Constants.Sqrt2*scale, x);
+            if (alpha == 1d && beta == 0d) return Cauchy.PDF(location, scale, x);
+
+            if (alpha == 0.5d && beta == 1d && x >= location)
+            {
+                return (Math.Sqrt(scale/Constants.Pi2)*Math.Exp(-scale/(2*(x - location))))/Math.Pow(x - location, 1.5);
+            }
+
+            throw new NotSupportedException();
+        }
+
+        /// <summary>
+        /// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
+        /// </summary>
+        /// <param name="alpha">The stability (α) of the distribution. Range: 2 ≥ α > 0.</param>
+        /// <param name="beta">The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.</param>
+        /// <param name="scale">The scale (c) of the distribution. Range: c > 0.</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 log density at <paramref name="x"/>.</returns>
+        /// <seealso cref="DensityLn"/>
+        public static double PDFLn(double alpha, double beta, double scale, double location, double x)
+        {
+            if (alpha <= 0.0 || alpha > 2.0 || beta < -1.0 || beta > 1.0 || scale <= 0.0)
+                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
+
+            if (alpha == 2d) return Normal.PDFLn(location, Constants.Sqrt2*scale, x);
+            if (alpha == 1d && beta == 0d) return Cauchy.PDFLn(location, scale, x);
+
+            if (alpha == 0.5d && beta == 1d && x >= location)
+            {
+                return (Math.Log(scale/Constants.Pi2))/2 - scale/(2*(x - location)) - 1.5*Math.Log(x - location);
+            }
+
+            throw new NotSupportedException();
+        }
+
+        /// <summary>
+        /// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
+        /// </summary>
+        /// <param name="x">The location at which to compute the cumulative distribution function.</param>
+        /// <param name="alpha">The stability (α) of the distribution. Range: 2 ≥ α > 0.</param>
+        /// <param name="beta">The skewness (β) of the distribution. Range: 1 ≥ β ≥ -1.</param>
+        /// <param name="scale">The scale (c) of the distribution. Range: c > 0.</param>
+        /// <param name="location">The location (μ) of the distribution.</param>
+        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
+        /// <seealso cref="CumulativeDistribution"/>
+        public static double CDF(double alpha, double beta, double scale, double location, double x)
+        {
+            if (alpha <= 0.0 || alpha > 2.0 || beta < -1.0 || beta > 1.0 || scale <= 0.0)
+                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
+
+            if (alpha == 2d) return Normal.CDF(location, Constants.Sqrt2*scale, x);
+            if (alpha == 1d && beta == 0d) return Cauchy.CDF(location, scale, x);
+
+            if (alpha == 0.5d && beta == 1d)
+            {
+                return SpecialFunctions.Erfc(Math.Sqrt(scale/(2*(x - location))));
+            }
+
+            throw new NotSupportedException();
+        }
 
         /// <summary>
         /// Generates a sample from the distribution.
@@ -465,10 +469,8 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a sample from the distribution.</returns>
         public static double Sample(System.Random rnd, double alpha, double beta, double scale, double location)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(alpha, beta, scale, location))
-            {
+            if (alpha <= 0.0 || alpha > 2.0 || beta < -1.0 || beta > 1.0 || scale <= 0.0)
                 throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
-            }
 
             return SampleUnchecked(rnd, alpha, beta, scale, location);
         }
@@ -484,10 +486,8 @@ namespace MathNet.Numerics.Distributions
         /// <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)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(location, scale, scale, location))
-            {
+            if (alpha <= 0.0 || alpha > 2.0 || beta < -1.0 || beta > 1.0 || scale <= 0.0)
                 throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
-            }
 
             while (true)
             {

src/Numerics/Distributions/StudentT.cs

@@ -38,7 +38,7 @@ namespace MathNet.Numerics.Distributions
     /// <summary>
     /// Continuous Univariate Student's T-distribution.
     /// Implements the univariate Student t-distribution. For details about this
-    /// distribution, see 
+    /// distribution, see
     /// <a href="http://en.wikipedia.org/wiki/Student%27s_t-distribution">
     /// Wikipedia - Student's t-distribution</a>.
     /// </summary>
@@ -50,7 +50,7 @@ namespace MathNet.Numerics.Distributions
     /// Gamma((dof+1)/2) (1 + (x - mu)^2 / (scale * scale * dof))^(-(dof+1)/2) /
     /// (Gamma(dof/2)*Sqrt(dof*pi*scale)).</para>
     /// <para>The distribution will use the <see cref="System.Random"/> by
-    /// default.  Users can get/set the random number generator by using the 
+    /// 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 range. This might involve heavy
@@ -66,18 +66,17 @@ namespace MathNet.Numerics.Distributions
 
         /// <summary>
         /// Initializes a new instance of the StudentT class. This is a Student t-distribution with location 0.0
-        /// scale 1.0 and degrees of freedom 1. The distribution will
-        /// be initialized with the default <seealso cref="System.Random"/> random number generator.
+        /// scale 1.0 and degrees of freedom 1.
         /// </summary>
         public StudentT()
-            : this(0.0, 1.0, 1.0)
         {
+            _random = MersenneTwister.Default;
+            SetParameters(0.0, 1.0, 1.0);
         }
 
         /// <summary>
         /// Initializes a new instance of the StudentT class with a particular location, scale and degrees of
-        /// freedom. The distribution will
-        /// be initialized with the default <seealso cref="System.Random"/> random number generator.
+        /// freedom.
         /// </summary>
         /// <param name="location">The location (μ) of the distribution.</param>
         /// <param name="scale">The scale (σ) of the distribution. Range: σ > 0.</param>
@@ -90,8 +89,7 @@ namespace MathNet.Numerics.Distributions
 
         /// <summary>
         /// Initializes a new instance of the StudentT class with a particular location, scale and degrees of
-        /// freedom. The distribution will
-        /// be initialized with the default <seealso cref="System.Random"/> random number generator.
+        /// freedom.
         /// </summary>
         /// <param name="location">The location (μ) of the distribution.</param>
         /// <param name="scale">The scale (σ) of the distribution. Range: σ > 0.</param>
@@ -112,18 +110,6 @@ namespace MathNet.Numerics.Distributions
             return "StudentT(μ = " + _location + ", σ = " + _scale + ", ν = " + _freedom + ")";
         }
 
-        /// <summary>
-        /// Checks whether the parameters of the distribution are valid. 
-        /// </summary>
-        /// <param name="location">The location (μ) of the distribution.</param>
-        /// <param name="scale">The scale (σ) of the distribution. Range: σ > 0.</param>
-        /// <param name="freedom">The degrees of freedom (ν) for the distribution. Range: ν > 0.</param>
-        /// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
-        static bool IsValidParameterSet(double location, double scale, double freedom)
-        {
-            return scale > 0.0 && freedom > 0.0 && !Double.IsNaN(location);
-        }
-
         /// <summary>
         /// Sets the parameters of the distribution after checking their validity.
         /// </summary>
@@ -133,7 +119,7 @@ namespace MathNet.Numerics.Distributions
         /// <exception cref="ArgumentOutOfRangeException">When the parameters are out of range.</exception>
         void SetParameters(double location, double scale, double freedom)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(location, scale, freedom))
+            if (scale <= 0.0 || freedom <= 0.0 || Double.IsNaN(scale) || Double.IsNaN(location) || Double.IsNaN(freedom))
             {
                 throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
             }
@@ -295,17 +281,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the density at <paramref name="x"/>.</returns>
         public double Density(double x)
         {
-            // TODO JVG we can probably do a better job for Cauchy special case
-            if (_freedom >= 1e+8d)
-            {
-                return Normal.PDF(_location, _scale, x);
-            }
-
-            var d = (x - _location)/_scale;
-            return Math.Exp(SpecialFunctions.GammaLn((_freedom + 1.0)/2.0) - SpecialFunctions.GammaLn(_freedom/2.0))
-                   *Math.Pow(1.0 + (d*d/_freedom), -0.5*(_freedom + 1.0))
-                   /Math.Sqrt(_freedom*Math.PI)
-                   /_scale;
+            return PDF(_location, _scale, _freedom, x);
         }
 
         /// <summary>
@@ -315,17 +291,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the log density at <paramref name="x"/>.</returns>
         public double DensityLn(double x)
         {
-            // TODO JVG we can probably do a better job for Cauchy special case
-            if (_freedom >= 1e+8d)
-            {
-                return Normal.PDFLn(_location, _scale, x);
-            }
-
-            var d = (x - _location)/_scale;
-            return SpecialFunctions.GammaLn((_freedom + 1.0)/2.0)
-                   - (0.5*((_freedom + 1.0)*Math.Log(1.0 + (d*d/_freedom))))
-                   - SpecialFunctions.GammaLn(_freedom/2.0)
-                   - (0.5*Math.Log(_freedom*Math.PI)) - Math.Log(_scale);
+            return PDFLn(_location, _scale, _freedom, x);
         }
 
         /// <summary>
@@ -335,22 +301,13 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
         public double CumulativeDistribution(double x)
         {
-            // TODO JVG we can probably do a better job for Cauchy special case
-            if (Double.IsPositiveInfinity(_freedom))
-            {
-                return Normal.CDF(_location, _scale, x);
-            }
-
-            var k = (x - _location)/_scale;
-            var h = _freedom/(_freedom + (k*k));
-            var ib = 0.5*SpecialFunctions.BetaRegularized(_freedom/2.0, 0.5, h);
-            return x <= _location ? ib : 1.0 - ib;
+            return CDF(_location, _scale, _freedom, x);
         }
 
         /// <summary>
         /// Samples student-t distributed random variables.
         /// </summary>
-        /// <remarks>The algorithm is method 2 in section 5, chapter 9 
+        /// <remarks>The algorithm is method 2 in section 5, chapter 9
         /// in L. Devroye's "Non-Uniform Random Variate Generation"</remarks>
         /// <param name="rnd">The random number generator to use.</param>
         /// <param name="location">The location (μ) of the distribution.</param>
@@ -384,6 +341,74 @@ namespace MathNet.Numerics.Distributions
             }
         }
 
+        /// <summary>
+        /// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
+        /// </summary>
+        /// <param name="location">The location (μ) of the distribution.</param>
+        /// <param name="scale">The scale (σ) of the distribution. Range: σ > 0.</param>
+        /// <param name="freedom">The degrees of freedom (ν) for the distribution. Range: ν > 0.</param>
+        /// <param name="x">The location at which to compute the density.</param>
+        /// <returns>the density at <paramref name="x"/>.</returns>
+        /// <seealso cref="Density"/>
+        public static double PDF(double location, double scale, double freedom, double x)
+        {
+            if (scale <= 0.0 || freedom <= 0.0) throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
+
+            // TODO JVG we can probably do a better job for Cauchy special case
+            if (freedom >= 1e+8d) return Normal.PDF(location, scale, x);
+
+            var d = (x - location)/scale;
+            return Math.Exp(SpecialFunctions.GammaLn((freedom + 1.0)/2.0) - SpecialFunctions.GammaLn(freedom/2.0))
+                   *Math.Pow(1.0 + (d*d/freedom), -0.5*(freedom + 1.0))
+                   /Math.Sqrt(freedom*Math.PI)
+                   /scale;
+        }
+
+        /// <summary>
+        /// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
+        /// </summary>
+        /// <param name="location">The location (μ) of the distribution.</param>
+        /// <param name="scale">The scale (σ) of the distribution. Range: σ > 0.</param>
+        /// <param name="freedom">The degrees of freedom (ν) for the distribution. Range: ν > 0.</param>
+        /// <param name="x">The location at which to compute the density.</param>
+        /// <returns>the log density at <paramref name="x"/>.</returns>
+        /// <seealso cref="DensityLn"/>
+        public static double PDFLn(double location, double scale, double freedom, double x)
+        {
+            if (scale <= 0.0 || freedom <= 0.0) throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
+
+            // TODO JVG we can probably do a better job for Cauchy special case
+            if (freedom >= 1e+8d) return Normal.PDFLn(location, scale, x);
+
+            var d = (x - location)/scale;
+            return SpecialFunctions.GammaLn((freedom + 1.0)/2.0)
+                   - (0.5*((freedom + 1.0)*Math.Log(1.0 + (d*d/freedom))))
+                   - SpecialFunctions.GammaLn(freedom/2.0)
+                   - (0.5*Math.Log(freedom*Math.PI)) - Math.Log(scale);
+        }
+
+        /// <summary>
+        /// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
+        /// </summary>
+        /// <param name="x">The location at which to compute the cumulative distribution function.</param>
+        /// <param name="location">The location (μ) of the distribution.</param>
+        /// <param name="scale">The scale (σ) of the distribution. Range: σ > 0.</param>
+        /// <param name="freedom">The degrees of freedom (ν) for the distribution. Range: ν > 0.</param>
+        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
+        /// <seealso cref="CumulativeDistribution"/>
+        public static double CDF(double location, double scale, double freedom, double x)
+        {
+            if (scale <= 0.0 || freedom <= 0.0) throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
+
+            // TODO JVG we can probably do a better job for Cauchy special case
+            if (Double.IsPositiveInfinity(freedom)) return Normal.CDF(location, scale, x);
+
+            var k = (x - location)/scale;
+            var h = freedom/(freedom + (k*k));
+            var ib = 0.5*SpecialFunctions.BetaRegularized(freedom/2.0, 0.5, h);
+            return x <= location ? ib : 1.0 - ib;
+        }
+
         /// <summary>
         /// Generates a sample from the Student t-distribution.
         /// </summary>
@@ -394,10 +419,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a sample from the distribution.</returns>
         public static double Sample(System.Random rnd, double location, double scale, double freedom)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(location, scale, freedom))
-            {
-                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
-            }
+            if (scale <= 0.0 || freedom <= 0.0) throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
 
             return SampleUnchecked(rnd, location, scale, freedom);
         }
@@ -412,10 +434,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a sequence of samples from the distribution.</returns>
         public static IEnumerable<double> Samples(System.Random rnd, double location, double scale, double freedom)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(location, scale, freedom))
-            {
-                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
-            }
+            if (scale <= 0.0 || freedom <= 0.0) throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
 
             while (true)
             {

src/Numerics/Distributions/Weibull.cs

@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2010 Math.NET
+// Copyright (c) 2009-2013 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -37,12 +37,12 @@ namespace MathNet.Numerics.Distributions
 {
     /// <summary>
     /// Continuous Univariate Weibull distribution.
-    /// For details about this distribution, see 
+    /// For details about this distribution, see
     /// <a href="http://en.wikipedia.org/wiki/Weibull_distribution">Wikipedia - Weibull distribution</a>.
     /// </summary>
     /// <remarks>
     /// <para>The Weibull distribution is parametrized by a shape and scale parameter.</para>
-    /// <para>The distribution will use the <see cref="System.Random"/> by default. 
+    /// <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
     /// range. This might involve heavy computation. Optionally, by setting Control.CheckDistributionParameters
@@ -95,17 +95,6 @@ namespace MathNet.Numerics.Distributions
             return "Weibull(k = " + _shape + ", λ = " + _scale + ")";
         }
 
-        /// <summary>
-        /// Checks whether the parameters of the distribution are valid. 
-        /// </summary>
-        /// <param name="shape">The shape (k) of the Weibull distribution. Range: k > 0.</param>
-        /// <param name="scale">The scale (λ) of the Weibull distribution. Range: λ > 0.</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)
-        {
-            return shape > 0.0 && scale > 0.0;
-        }
-
         /// <summary>
         /// Sets the parameters of the distribution after checking their validity.
         /// </summary>
@@ -114,7 +103,7 @@ namespace MathNet.Numerics.Distributions
         /// <exception cref="ArgumentOutOfRangeException">When the parameters are out of range.</exception>
         void SetParameters(double shape, double scale)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(shape, scale))
+            if (shape <= 0.0 || scale <= 0.0 || Double.IsNaN(shape) || Double.IsNaN(scale))
             {
                 throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
             }
@@ -285,10 +274,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
         public double CumulativeDistribution(double x)
         {
-            if (x < 0.0)
-            {
-                return 0.0;
-            }
+            if (x < 0.0) return 0.0;
 
             return -SpecialFunctions.ExponentialMinusOne(-Math.Pow(x, _shape)*_scalePowShapeInv);
         }
@@ -328,6 +314,79 @@ namespace MathNet.Numerics.Distributions
             }
         }
 
+        /// <summary>
+        /// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
+        /// </summary>
+        /// <param name="shape">The shape (k) of the Weibull distribution. Range: k > 0.</param>
+        /// <param name="scale">The scale (λ) of the Weibull distribution. Range: λ > 0.</param>
+        /// <param name="x">The location at which to compute the density.</param>
+        /// <returns>the density at <paramref name="x"/>.</returns>
+        /// <seealso cref="Density"/>
+        public static double PDF(double shape, double scale, double x)
+        {
+            if (shape <= 0.0 || scale <= 0.0) throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
+
+            if (x >= 0.0)
+            {
+                if (x == 0.0 && shape == 1.0)
+                {
+                    return shape/scale;
+                }
+
+                return shape
+                       *Math.Pow(x/scale, shape - 1.0)
+                       *Math.Exp(-Math.Pow(x, shape)*Math.Pow(scale, -shape))
+                       /scale;
+            }
+
+            return 0.0;
+        }
+
+        /// <summary>
+        /// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
+        /// </summary>
+        /// <param name="shape">The shape (k) of the Weibull distribution. Range: k > 0.</param>
+        /// <param name="scale">The scale (λ) of the Weibull distribution. Range: λ > 0.</param>
+        /// <param name="x">The location at which to compute the density.</param>
+        /// <returns>the log density at <paramref name="x"/>.</returns>
+        /// <seealso cref="DensityLn"/>
+        public static double PDFLn(double shape, double scale, double x)
+        {
+            if (shape <= 0.0 || scale <= 0.0) throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
+
+            if (x >= 0.0)
+            {
+                if (x == 0.0 && shape == 1.0)
+                {
+                    return Math.Log(shape) - Math.Log(scale);
+                }
+
+                return Math.Log(shape)
+                       + ((shape - 1.0)*Math.Log(x/scale))
+                       - (Math.Pow(x, shape)*Math.Pow(scale, -shape))
+                       - Math.Log(scale);
+            }
+
+            return double.NegativeInfinity;
+        }
+
+        /// <summary>
+        /// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
+        /// </summary>
+        /// <param name="x">The location at which to compute the cumulative distribution function.</param>
+        /// <param name="shape">The shape (k) of the Weibull distribution. Range: k > 0.</param>
+        /// <param name="scale">The scale (λ) of the Weibull distribution. Range: λ > 0.</param>
+        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
+        /// <seealso cref="CumulativeDistribution"/>
+        public static double CDF(double shape, double scale, double x)
+        {
+            if (shape <= 0.0 || scale <= 0.0) throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
+
+            if (x < 0.0) return 0.0;
+
+            return -SpecialFunctions.ExponentialMinusOne(-Math.Pow(x, shape)*Math.Pow(scale, -shape));
+        }
+
         /// <summary>
         /// Generates a sample from the Weibull distribution.
         /// </summary>
@@ -337,10 +396,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a sample from the distribution.</returns>
         public static double Sample(System.Random rnd, double shape, double scale)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(shape, scale))
-            {
-                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
-            }
+            if (shape <= 0.0 || scale <= 0.0) throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
 
             return SampleUnchecked(rnd, shape, scale);
         }
@@ -354,10 +410,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>a sequence of samples from the distribution.</returns>
         public static IEnumerable<double> Samples(System.Random rnd, double shape, double scale)
         {
-            if (Control.CheckDistributionParameters && !IsValidParameterSet(shape, scale))
-            {
-                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
-            }
+            if (shape <= 0.0 || scale <= 0.0) throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
 
             while (true)
             {

src/UnitTests/DistributionTests/Continuous/StudentTTests.cs

@@ -390,25 +390,6 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Continuous
             ied.Take(5).ToArray();
         }
 
-        /// <summary>
-        /// Fail sample static with bad parameters.
-        /// </summary>
-        [Test]
-        public void FailSampleStatic()
-        {
-            Assert.Throws<ArgumentOutOfRangeException>(() => StudentT.Sample(new Random(0), Double.NaN, 1.0, Double.NaN));
-        }
-
-        /// <summary>
-        /// Fail sample sequence static with bad parameters.
-        /// </summary>
-        [Test]
-        public void FailSampleSequenceStatic()
-        {
-            var ied = StudentT.Samples(new Random(0), 0.0, 1.0, Double.NaN);
-            Assert.Throws<ArgumentOutOfRangeException>(() => ied.Take(5).ToArray());
-        }
-
         /// <summary>
         /// Can sample.
         /// </summary>