Distributions: static PMF, PMFLn, CDF functions for discrete distributions

src/FSharp/Distributions.fs

@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2012 Math.NET
+// Copyright (c) 2009-2014 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -56,8 +56,8 @@ module Sample =
     let binomialSeq p n rng = Binomial.Samples(rng, p, n)
 
     /// Categorical with an array of nonnegative ratios defining the relative probability mass (unnormalized).
-    let categorical probabilityMass rng = Categorical.SampleWithProbabilityMass(rng, probabilityMass)
-    let categoricalSeq probabilityMass rng = Categorical.SamplesWithProbabilityMass(rng, probabilityMass)
+    let categorical probabilityMass rng = Categorical.Sample(rng, probabilityMass)
+    let categoricalSeq probabilityMass rng = Categorical.Samples(rng, probabilityMass)
 
     /// Cauchy with location (x0) and scale (γ).
     let cauchy location scale rng = Cauchy.Sample(rng, location, scale)
@@ -119,7 +119,7 @@ module Sample =
     let logNormal mu sigma rng = LogNormal.Sample(rng, mu, sigma)
     let logNormalSeq mu sigma rng = LogNormal.Samples(rng, mu, sigma)
 
-    /// Negative-Binomial with number of failures (r) until the experiment stoppedand probability (p) of a trial resulting in success.
+    /// Negative-Binomial with number of failures (r) until the experiment stopped and probability (p) of a trial resulting in success.
     let negativeBinomial r p rng = NegativeBinomial.Sample(rng, r, p)
     let negativeBinomialSeq r p rng = NegativeBinomial.Samples(rng, r, p)
 

src/Numerics/Distributions/Bernoulli.cs

@@ -191,16 +191,8 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the probability mass at location <paramref name="k"/>.</returns>
         public double Probability(int k)
         {
-            if (k == 0)
-            {
-                return 1.0 - _p;
-            }
-
-            if (k == 1)
-            {
-                return _p;
-            }
-
+            if (k == 0) return 1.0 - _p;
+            if (k == 1) return _p;
             return 0.0;
         }
 
@@ -211,11 +203,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
         public double ProbabilityLn(int k)
         {
-            if (k == 0)
-            {
-                return Math.Log(1.0 - _p);
-            }
-
+            if (k == 0) return Math.Log(1.0 - _p);
             return k == 1 ? Math.Log(_p) : Double.NegativeInfinity;
         }
 
@@ -226,17 +214,51 @@ 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;
+            if (x >= 1.0) return 1.0;
+            return 1.0 - _p;
+        }
 
-            if (x < 1.0)
-            {
-                return 1.0 - _p;
-            }
+        /// <summary>
+        /// Computes the probability mass (PMF) at k, i.e. P(X = k).
+        /// </summary>
+        /// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
+        /// <param name="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
+        /// <returns>the probability mass at location <paramref name="k"/>.</returns>
+        public static double PMF(double p, int k)
+        {
+            if (!(p >= 0.0 && p <= 1.0)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+            if (k == 0) return 1.0 - p;
+            if (k == 1) return p;
+            return 0.0;
+        }
 
-            return 1.0;
+        /// <summary>
+        /// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
+        /// </summary>
+        /// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
+        /// <param name="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
+        /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
+        public static double PMFLn(double p, int k)
+        {
+            if (!(p >= 0.0 && p <= 1.0)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+            if (k == 0) return Math.Log(1.0 - p);
+            return k == 1 ? Math.Log(p) : 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="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
+        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
+        /// <seealso cref="CumulativeDistribution"/>
+        public static double CDF(double p, double x)
+        {
+            if (!(p >= 0.0 && p <= 1.0)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+            if (x < 0.0) return 0.0;
+            if (x >= 1.0) return 1.0;
+            return 1.0 - p;
         }
 
         /// <summary>

src/Numerics/Distributions/Binomial.cs

@@ -228,14 +228,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the probability mass at location <paramref name="k"/>.</returns>
         public double Probability(int k)
         {
-            if (k < 0) return 0.0;
-            if (k > _trials) return 0.0;
-            if (_p == 0.0 && k == 0) return 1.0;
-            if (_p == 0.0) return 0.0;
-            if (_p == 1.0 && k == _trials) return 1.0;
-            if (_p == 1.0) return 0.0;
-
-            return SpecialFunctions.Binomial(_trials, k)*Math.Pow(_p, k)*Math.Pow(1.0 - _p, _trials - k);
+            return PMF(_p, _trials, k);
         }
 
         /// <summary>
@@ -245,14 +238,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
         public double ProbabilityLn(int k)
         {
-            if (k < 0) return Double.NegativeInfinity;
-            if (k > _trials) return Double.NegativeInfinity;
-            if (_p == 0.0 && k == 0) return 0.0;
-            if (_p == 0.0) return Double.NegativeInfinity;
-            if (_p == 1.0 && k == _trials) return 0.0;
-            if (_p == 1.0) return Double.NegativeInfinity;
-
-            return SpecialFunctions.BinomialLn(_trials, k) + (k*Math.Log(_p)) + ((_trials - k)*Math.Log(1.0 - _p));
+            return PMFLn(_p, _trials, k);
         }
 
         /// <summary>
@@ -262,11 +248,56 @@ 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 > _trials) return 1.0;
+            return CDF(_p, _trials, x);
+        }
+
+        /// <summary>
+        /// Computes the probability mass (PMF) at k, i.e. P(X = k).
+        /// </summary>
+        /// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
+        /// <param name="p">The success probability (p) in each trial. Range: 0 ≤ p ≤ 1.</param>
+        /// <param name="n">The number of trials (n). Range: n ≥ 0.</param>
+        /// <returns>the probability mass at location <paramref name="k"/>.</returns>
+        public static double PMF(double p, int n, int k)
+        {
+            if (!(p >= 0.0 && p <= 1.0 && n >= 0)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+            if (k < 0 || k > n) return 0.0;
+            if (p == 0.0) return k == 0 ? 1.0 : 0.0;
+            if (p == 1.0) return k == n ? 1.0 : 0.0;
+            return Math.Exp(SpecialFunctions.BinomialLn(n, k) + (k*Math.Log(p)) + ((n - k)*Math.Log(1.0 - p)));
+        }
+
+        /// <summary>
+        /// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
+        /// </summary>
+        /// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
+        /// <param name="p">The success probability (p) in each trial. Range: 0 ≤ p ≤ 1.</param>
+        /// <param name="n">The number of trials (n). Range: n ≥ 0.</param>
+        /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
+        public static double PMFLn(double p, int n, int k)
+        {
+            if (!(p >= 0.0 && p <= 1.0 && n >= 0)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+            if (k < 0 || k > n) return Double.NegativeInfinity;
+            if (p == 0.0) return k == 0 ? 0.0 : Double.NegativeInfinity;
+            if (p == 1.0) return k == n ? 0.0 : Double.NegativeInfinity;
+            return SpecialFunctions.BinomialLn(n, k) + (k*Math.Log(p)) + ((n - k)*Math.Log(1.0 - p));
+        }
 
+        /// <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="p">The success probability (p) in each trial. Range: 0 ≤ p ≤ 1.</param>
+        /// <param name="n">The number of trials (n). Range: n ≥ 0.</param>
+        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
+        /// <seealso cref="CumulativeDistribution"/>
+        public static double CDF(double p, int n, double x)
+        {
+            if (!(p >= 0.0 && p <= 1.0 && n >= 0)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+            if (x < 0.0) return 0.0;
+            if (x > n) return 1.0;
             double k = Math.Floor(x);
-            return SpecialFunctions.BetaRegularized(_trials - k, k + 1, 1 - _p);
+            return SpecialFunctions.BetaRegularized(n - k, k + 1, 1 - p);
         }
 
         /// <summary>

src/Numerics/Distributions/Categorical.cs

@@ -4,7 +4,7 @@
 // http://github.com/mathnet/mathnet-numerics
 // http://mathnetnumerics.codeplex.com
 //
-// Copyright (c) 2009-2013 Math.NET
+// Copyright (c) 2009-2014 Math.NET
 //
 // Permission is hereby granted, free of charge, to any person
 // obtaining a copy of this software and associated documentation
@@ -365,6 +365,91 @@ namespace MathNet.Numerics.Distributions
             return idx;
         }
 
+        /// <summary>
+        /// Computes the probability mass (PMF) at k, i.e. P(X = k).
+        /// </summary>
+        /// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
+        /// <param name="probabilityMass">An array of nonnegative ratios: this array does not need to be normalized
+        /// as this is often impossible using floating point arithmetic.</param>
+        /// <returns>the probability mass at location <paramref name="k"/>.</returns>
+        public static double PMF(double[] probabilityMass, int k)
+        {
+            if (Control.CheckDistributionParameters && !IsValidProbabilityMass(probabilityMass))
+            {
+                throw new ArgumentException(Resources.InvalidDistributionParameters);
+            }
+
+            if (k < 0) return 0.0;
+            if (k >= probabilityMass.Length) return 0.0;
+
+            return probabilityMass[k]/probabilityMass.Sum();
+        }
+
+        /// <summary>
+        /// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
+        /// </summary>
+        /// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
+        /// <param name="probabilityMass">An array of nonnegative ratios: this array does not need to be normalized
+        /// as this is often impossible using floating point arithmetic.</param>
+        /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
+        public static double PMFLn(double[] probabilityMass, int k)
+        {
+            return Math.Log(PMF(probabilityMass, k));
+        }
+
+        /// <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="probabilityMass">An array of nonnegative ratios: this array does not need to be normalized
+        /// as this is often impossible using floating point arithmetic.</param>
+        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
+        /// <seealso cref="CumulativeDistribution"/>
+        public static double CDF(double[] probabilityMass, double x)
+        {
+            if (Control.CheckDistributionParameters && !IsValidProbabilityMass(probabilityMass))
+            {
+                throw new ArgumentException(Resources.InvalidDistributionParameters);
+            }
+
+            if (x < 0.0) return 0.0;
+            if (x >= probabilityMass.Length) return 1.0;
+
+            var cdfUnnormalized = ProbabilityMassToCumulativeDistribution(probabilityMass);
+            return cdfUnnormalized[(int)Math.Floor(x)]/cdfUnnormalized[cdfUnnormalized.Length - 1];
+        }
+
+        /// <summary>
+        /// Computes the inverse of the cumulative distribution function (InvCDF) for the distribution
+        /// at the given probability.
+        /// </summary>
+        /// <param name="probabilityMass">An array of nonnegative ratios: this array does not need to be normalized
+        /// as this is often impossible using floating point arithmetic.</param>
+        /// <param name="probability">A real number between 0 and 1.</param>
+        /// <returns>An integer between 0 and the size of the categorical (exclusive), that corresponds to the inverse CDF for the given probability.</returns>
+        public static int InvCDF(double[] probabilityMass, double probability)
+        {
+            if (Control.CheckDistributionParameters && !IsValidProbabilityMass(probabilityMass))
+            {
+                throw new ArgumentException(Resources.InvalidDistributionParameters);
+            }
+
+            if (probability < 0.0 || probability > 1.0 || Double.IsNaN(probability))
+            {
+                throw new ArgumentOutOfRangeException("probability");
+            }
+
+            var cdfUnnormalized = ProbabilityMassToCumulativeDistribution(probabilityMass);
+            var denormalizedProbability = probability * cdfUnnormalized[cdfUnnormalized.Length - 1];
+            int idx = Array.BinarySearch(cdfUnnormalized, denormalizedProbability);
+            if (idx < 0)
+            {
+                idx = ~idx;
+            }
+
+            return idx;
+        }
+
         /// <summary>
         /// Computes the inverse of the cumulative distribution function (InvCDF) for the distribution
         /// at the given probability.
@@ -372,7 +457,7 @@ namespace MathNet.Numerics.Distributions
         /// <param name="cdfUnnormalized">An array corresponding to a CDF for a categorical distribution. Not assumed to be normalized.</param>
         /// <param name="probability">A real number between 0 and 1.</param>
         /// <returns>An integer between 0 and the size of the categorical (exclusive), that corresponds to the inverse CDF for the given probability.</returns>
-        public static int InverseCumulativeDistribution(double[] cdfUnnormalized, double probability)
+        public static int InvCDFWithCumulativeDistribution(double[] cdfUnnormalized, double probability)
         {
             if (Control.CheckDistributionParameters && !IsValidCumulativeDistribution(cdfUnnormalized))
             {
@@ -398,16 +483,16 @@ namespace MathNet.Numerics.Distributions
         /// Computes the cumulative distribution function. This method performs no parameter checking.
         /// If the probability mass was normalized, the resulting cumulative distribution is normalized as well (up to numerical errors).
         /// </summary>
-        /// <param name="pmfUnnormalized">An array of nonnegative ratios: this array does not need to be normalized
+        /// <param name="probabilityMass">An array of nonnegative ratios: this array does not need to be normalized
         /// as this is often impossible using floating point arithmetic.</param>
         /// <returns>An array representing the unnormalized cumulative distribution function.</returns>
-        internal static double[] ProbabilityMassToCumulativeDistribution(double[] pmfUnnormalized)
+        internal static double[] ProbabilityMassToCumulativeDistribution(double[] probabilityMass)
         {
-            var cdfUnnormalized = new double[pmfUnnormalized.Length];
-            cdfUnnormalized[0] = pmfUnnormalized[0];
-            for (int i = 1; i < pmfUnnormalized.Length; i++)
+            var cdfUnnormalized = new double[probabilityMass.Length];
+            cdfUnnormalized[0] = probabilityMass[0];
+            for (int i = 1; i < probabilityMass.Length; i++)
             {
-                cdfUnnormalized[i] = cdfUnnormalized[i - 1] + pmfUnnormalized[i];
+                cdfUnnormalized[i] = cdfUnnormalized[i - 1] + probabilityMass[i];
             }
 
             return cdfUnnormalized;
@@ -458,71 +543,71 @@ namespace MathNet.Numerics.Distributions
         /// Samples one categorical distributed random variable; also known as the Discrete distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="cdfUnnormalized">An array of the cumulative distribution. Not assumed to be normalized.</param>
+        /// <param name="probabilityMass">An array of nonnegative ratios. Not assumed to be normalized.</param>
         /// <returns>One random integer between 0 and the size of the categorical (exclusive).</returns>
-        public static int SampleWithCumulativeDistribution(System.Random rnd, double[] cdfUnnormalized)
+        public static int Sample(System.Random rnd, double[] probabilityMass)
         {
-            if (Control.CheckDistributionParameters && !IsValidCumulativeDistribution(cdfUnnormalized))
+            if (Control.CheckDistributionParameters && !IsValidProbabilityMass(probabilityMass))
             {
                 throw new ArgumentException(Resources.InvalidDistributionParameters);
             }
 
-            return SampleUnchecked(rnd, cdfUnnormalized);
+            var cdf = ProbabilityMassToCumulativeDistribution(probabilityMass);
+            return SampleUnchecked(rnd, cdf);
         }
 
         /// <summary>
-        /// Samples one categorical distributed random variable; also known as the Discrete distribution.
+        /// Samples a categorically distributed random variable.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="pmfUnnormalized">An array of nonnegative ratios. Not assumed to be normalized.</param>
-        /// <returns>One random integer between 0 and the size of the categorical (exclusive).</returns>
-        public static int SampleWithProbabilityMass(System.Random rnd, double[] pmfUnnormalized)
+        /// <param name="probabilityMass">An array of nonnegative ratios. Not assumed to be normalized.</param>
+        /// <returns>random integers between 0 and the size of the categorical (exclusive).</returns>
+        public static IEnumerable<int> Samples(System.Random rnd, double[] probabilityMass)
         {
-            if (Control.CheckDistributionParameters && !IsValidProbabilityMass(pmfUnnormalized))
+            if (Control.CheckDistributionParameters && !IsValidProbabilityMass(probabilityMass))
             {
                 throw new ArgumentException(Resources.InvalidDistributionParameters);
             }
 
-            var cdf = ProbabilityMassToCumulativeDistribution(pmfUnnormalized);
-            return SampleUnchecked(rnd, cdf);
+            var cdf = ProbabilityMassToCumulativeDistribution(probabilityMass);
+            while (true)
+            {
+                yield return SampleUnchecked(rnd, cdf);
+            }
         }
 
         /// <summary>
-        /// Samples a categorically distributed random variable.
+        /// Samples one categorical distributed random variable; also known as the Discrete distribution.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
         /// <param name="cdfUnnormalized">An array of the cumulative distribution. Not assumed to be normalized.</param>
-        /// <returns>random integers between 0 and the size of the categorical (exclusive).</returns>
-        public static IEnumerable<int> SamplesWithCumulativeDistribution(System.Random rnd, double[] cdfUnnormalized)
+        /// <returns>One random integer between 0 and the size of the categorical (exclusive).</returns>
+        public static int SampleWithCumulativeDistribution(System.Random rnd, double[] cdfUnnormalized)
         {
             if (Control.CheckDistributionParameters && !IsValidCumulativeDistribution(cdfUnnormalized))
             {
                 throw new ArgumentException(Resources.InvalidDistributionParameters);
             }
 
-            while (true)
-            {
-                yield return SampleUnchecked(rnd, cdfUnnormalized);
-            }
+            return SampleUnchecked(rnd, cdfUnnormalized);
         }
 
         /// <summary>
         /// Samples a categorically distributed random variable.
         /// </summary>
         /// <param name="rnd">The random number generator to use.</param>
-        /// <param name="pmfUnnormalized">An array of nonnegative ratios. Not assumed to be normalized.</param>
+        /// <param name="cdfUnnormalized">An array of the cumulative distribution. Not assumed to be normalized.</param>
         /// <returns>random integers between 0 and the size of the categorical (exclusive).</returns>
-        public static IEnumerable<int> SamplesWithProbabilityMass(System.Random rnd, double[] pmfUnnormalized)
+        public static IEnumerable<int> SamplesWithCumulativeDistribution(System.Random rnd, double[] cdfUnnormalized)
         {
-            if (Control.CheckDistributionParameters && !IsValidProbabilityMass(pmfUnnormalized))
+            if (Control.CheckDistributionParameters && !IsValidCumulativeDistribution(cdfUnnormalized))
             {
                 throw new ArgumentException(Resources.InvalidDistributionParameters);
             }
 
-            var cdf = ProbabilityMassToCumulativeDistribution(pmfUnnormalized);
             while (true)
             {
-                yield return SampleUnchecked(rnd, cdf);
+                yield return SampleUnchecked(rnd, cdfUnnormalized);
             }
         }
     }

src/Numerics/Distributions/ConwayMaxwellPoisson.cs

@@ -347,7 +347,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
         public double ProbabilityLn(int k)
         {
-            return Math.Log(Probability(k));
+            return k*Math.Log(_lambda) - _nu*SpecialFunctions.FactorialLn(k) - Math.Log(Z);
         }
 
         /// <summary>
@@ -357,12 +357,63 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
         public double CumulativeDistribution(double x)
         {
+            var z = Z;
             double sum = 0;
             for (var i = 0; i < x + 1; i++)
             {
-                sum += Probability(i);
+                sum += Math.Pow(_lambda, i)/Math.Pow(SpecialFunctions.Factorial(i), _nu)/z;
             }
+            return sum;
+        }
+
+        /// <summary>
+        /// Computes the probability mass (PMF) at k, i.e. P(X = k).
+        /// </summary>
+        /// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
+        /// <param name="lambda">The lambda (λ) parameter. Range: λ > 0.</param>
+        /// <param name="nu">The rate of decay (ν) parameter. Range: ν ≥ 0.</param>
+        /// <returns>the probability mass at location <paramref name="k"/>.</returns>
+        public static double PMF(double lambda, double nu, int k)
+        {
+            if (!(lambda > 0.0 && nu >= 0.0)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+
+            var z = Normalization(lambda, nu);
+            return Math.Pow(lambda, k)/Math.Pow(SpecialFunctions.Factorial(k), nu)/z;
+        }
 
+        /// <summary>
+        /// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
+        /// </summary>
+        /// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
+        /// <param name="lambda">The lambda (λ) parameter. Range: λ > 0.</param>
+        /// <param name="nu">The rate of decay (ν) parameter. Range: ν ≥ 0.</param>
+        /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
+        public static double PMFLn(double lambda, double nu, int k)
+        {
+            if (!(lambda > 0.0 && nu >= 0.0)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+
+            var z = Normalization(lambda, nu);
+            return k*Math.Log(lambda) - nu*SpecialFunctions.FactorialLn(k) - Math.Log(z);
+        }
+
+        /// <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="lambda">The lambda (λ) parameter. Range: λ > 0.</param>
+        /// <param name="nu">The rate of decay (ν) parameter. Range: ν ≥ 0.</param>
+        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
+        /// <seealso cref="CumulativeDistribution"/>
+        public static double CDF(double lambda, double nu, double x)
+        {
+            if (!(lambda > 0.0 && nu >= 0.0)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+
+            var z = Normalization(lambda, nu);
+            double sum = 0;
+            for (var i = 0; i < x + 1; i++)
+            {
+                sum += Math.Pow(lambda, i)/Math.Pow(SpecialFunctions.Factorial(i), nu)/z;
+            }
             return sum;
         }
 

src/Numerics/Distributions/DiscreteUniform.cs

@@ -205,12 +205,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the probability mass at location <paramref name="k"/>.</returns>
         public double Probability(int k)
         {
-            if (k >= _lower && k <= _upper)
-            {
-                return 1.0/(_upper - _lower + 1);
-            }
-
-            return 0.0;
+            return PMF(_lower, _upper, k);
         }
 
         /// <summary>
@@ -220,12 +215,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
         public double ProbabilityLn(int k)
         {
-            if (k >= _lower && k <= _upper)
-            {
-                return -Math.Log(_upper - _lower + 1);
-            }
-
-            return Double.NegativeInfinity;
+            return PMFLn(_lower, _upper, k);
         }
 
         /// <summary>
@@ -235,17 +225,53 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
         public double CumulativeDistribution(double x)
         {
-            if (x < _lower)
-            {
-                return 0.0;
-            }
+            return CDF(_lower, _upper, x);
+        }
 
-            if (x >= _upper)
-            {
-                return 1.0;
-            }
+        /// <summary>
+        /// Computes the probability mass (PMF) at k, i.e. P(X = k).
+        /// </summary>
+        /// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
+        /// <param name="lower">Lower bound. Range: lower ≤ upper.</param>
+        /// <param name="upper">Upper bound. Range: lower ≤ upper.</param>
+        /// <returns>the probability mass at location <paramref name="k"/>.</returns>
+        public static double PMF(int lower, int upper, int k)
+        {
+            if (!(lower <= upper)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+
+            return k >= lower && k <= upper ? 1.0/(upper - lower + 1) : 0.0;
+        }
+
+        /// <summary>
+        /// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
+        /// </summary>
+        /// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
+        /// <param name="lower">Lower bound. Range: lower ≤ upper.</param>
+        /// <param name="upper">Upper bound. Range: lower ≤ upper.</param>
+        /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
+        public static double PMFLn(int lower, int upper, int k)
+        {
+            if (!(lower <= upper)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+
+            return k >= lower && k <= upper ? -Math.Log(upper - lower + 1) : 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="lower">Lower bound. Range: lower ≤ upper.</param>
+        /// <param name="upper">Upper bound. Range: lower ≤ upper.</param>
+        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
+        /// <seealso cref="CumulativeDistribution"/>
+        public static double CDF(int lower, int upper, double x)
+        {
+            if (!(lower <= upper)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+
+            if (x < lower) return 0.0;
+            if (x >= upper) return 1.0;
 
-            return Math.Min(1.0, (Math.Floor(x) - _lower + 1)/(_upper - _lower + 1));
+            return Math.Min(1.0, (Math.Floor(x) - lower + 1)/(upper - lower + 1));
         }
 
         /// <summary>

src/Numerics/Distributions/Geometric.cs

@@ -190,11 +190,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the probability mass at location <paramref name="k"/>.</returns>
         public double Probability(int k)
         {
-            if (k <= 0)
-            {
-                return 0.0;
-            }
-
+            if (k <= 0) return 0.0;
             return Math.Pow(1.0 - _p, k - 1)*_p;
         }
 
@@ -205,11 +201,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
         public double ProbabilityLn(int k)
         {
-            if (k <= 0)
-            {
-                return Double.NegativeInfinity;
-            }
-
+            if (k <= 0) return Double.NegativeInfinity;
             return ((k - 1)*Math.Log(1.0 - _p)) + Math.Log(_p);
         }
 
@@ -223,6 +215,45 @@ namespace MathNet.Numerics.Distributions
             return 1.0 - Math.Pow(1.0 - _p, x);
         }
 
+        /// <summary>
+        /// Computes the probability mass (PMF) at k, i.e. P(X = k).
+        /// </summary>
+        /// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
+        /// <param name="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
+        /// <returns>the probability mass at location <paramref name="k"/>.</returns>
+        public static double PMF(double p, int k)
+        {
+            if (!(p >= 0.0 && p <= 1.0)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+            if (k <= 0) return 0.0;
+            return Math.Pow(1.0 - p, k - 1)*p;
+        }
+
+        /// <summary>
+        /// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
+        /// </summary>
+        /// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
+        /// <param name="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
+        /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
+        public static double PMFLn(double p, int k)
+        {
+            if (!(p >= 0.0 && p <= 1.0)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+            if (k <= 0) return Double.NegativeInfinity;
+            return ((k - 1)*Math.Log(1.0 - p)) + Math.Log(p);
+        }
+
+        /// <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="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
+        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
+        /// <seealso cref="CumulativeDistribution"/>
+        public static double CDF(double p, double x)
+        {
+            if (!(p >= 0.0 && p <= 1.0)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+            return 1.0 - Math.Pow(1.0 - p, x);
+        }
+
         /// <summary>
         /// Returns one sample from the distribution.
         /// </summary>

src/Numerics/Distributions/Hypergeometric.cs

@@ -260,7 +260,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
         public double ProbabilityLn(int k)
         {
-            return Math.Log(Probability(k));
+            return SpecialFunctions.BinomialLn(_success, k) + SpecialFunctions.BinomialLn(_population - _success, _draws - k) - SpecialFunctions.BinomialLn(_population, _draws);
         }
 
         /// <summary>
@@ -270,21 +270,70 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
         public double CumulativeDistribution(double x)
         {
-            if (x < Minimum)
+            return CDF(_population, _success, _draws, x);
+        }
+
+        /// <summary>
+        /// Computes the probability mass (PMF) at k, i.e. P(X = k).
+        /// </summary>
+        /// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
+        /// <param name="population">The size of the population (N).</param>
+        /// <param name="success">The number successes within the population (K, M).</param>
+        /// <param name="draws">The number of draws without replacement (n).</param>
+        /// <returns>the probability mass at location <paramref name="k"/>.</returns>
+        public static double PMF(int population, int success, int draws, int k)
+        {
+            if (!(population >= 0 && success >= 0 && draws >= 0 && success <= population && draws <= population))
+            {
+                throw new ArgumentException(Resources.InvalidDistributionParameters);
+            }
+
+            return SpecialFunctions.Binomial(success, k)*SpecialFunctions.Binomial(population - success, draws - k)/SpecialFunctions.Binomial(population, draws);
+        }
+
+        /// <summary>
+        /// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
+        /// </summary>
+        /// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
+        /// <param name="population">The size of the population (N).</param>
+        /// <param name="success">The number successes within the population (K, M).</param>
+        /// <param name="draws">The number of draws without replacement (n).</param>
+        /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
+        public static double PMFLn(int population, int success, int draws, int k)
+        {
+            if (!(population >= 0 && success >= 0 && draws >= 0 && success <= population && draws <= population))
             {
-                return 0.0;
+                throw new ArgumentException(Resources.InvalidDistributionParameters);
             }
-            if (x >= Maximum)
+
+            return SpecialFunctions.BinomialLn(success, k) + SpecialFunctions.BinomialLn(population - success, draws - k) - SpecialFunctions.BinomialLn(population, draws);
+        }
+
+        /// <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="population">The size of the population (N).</param>
+        /// <param name="success">The number successes within the population (K, M).</param>
+        /// <param name="draws">The number of draws without replacement (n).</param>
+        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
+        /// <seealso cref="CumulativeDistribution"/>
+        public static double CDF(int population, int success, int draws, double x)
+        {
+            if (!(population >= 0 && success >= 0 && draws >= 0 && success <= population && draws <= population))
             {
-                return 1.0;
+                throw new ArgumentException(Resources.InvalidDistributionParameters);
             }
 
+            if (x < Math.Max(0, draws + success - population)) return 0.0;
+            if (x >= Math.Min(success, draws)) return 1.0;
+
             var k = (int)Math.Floor(x);
-            var denominatorLn = SpecialFunctions.BinomialLn(_population, _draws);
+            var denominatorLn = SpecialFunctions.BinomialLn(population, draws);
             var sum = 0.0;
             for (var i = 0; i <= k; i++)
             {
-                sum += Math.Exp(SpecialFunctions.BinomialLn(_success, i) + SpecialFunctions.BinomialLn(_population - _success, _draws - i) - denominatorLn);
+                sum += Math.Exp(SpecialFunctions.BinomialLn(success, i) + SpecialFunctions.BinomialLn(population - success, draws - i) - denominatorLn);
             }
             return sum;
         }

src/Numerics/Distributions/NegativeBinomial.cs

@@ -206,12 +206,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the probability mass at location <paramref name="k"/>.</returns>
         public double Probability(int k)
         {
-            var ln = SpecialFunctions.GammaLn(_trials + k)
-                     - SpecialFunctions.GammaLn(_trials)
-                     - SpecialFunctions.GammaLn(k + 1.0)
-                     + (_trials*Math.Log(_p))
-                     + (k*Math.Log(1.0 - _p));
-            return Math.Exp(ln);
+            return PMF(_trials, _p, k);
         }
 
         /// <summary>
@@ -221,12 +216,7 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
         public double ProbabilityLn(int k)
         {
-            var ln = SpecialFunctions.GammaLn(_trials + k)
-                     - SpecialFunctions.GammaLn(_trials)
-                     - SpecialFunctions.GammaLn(k + 1.0)
-                     + (_trials*Math.Log(_p))
-                     + (k*Math.Log(1.0 - _p));
-            return ln;
+            return PMFLn(_trials, _p, k);
         }
 
         /// <summary>
@@ -236,7 +226,52 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
         public double CumulativeDistribution(double x)
         {
-            return 1 - SpecialFunctions.BetaRegularized(x + 1, _trials, 1 - _p);
+            return CDF(_trials, _p, x);
+        }
+
+        /// <summary>
+        /// Computes the probability mass (PMF) at k, i.e. P(X = k).
+        /// </summary>
+        /// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
+        /// <param name="r">The number of failures (r) until the experiment stopped. Range: r ≥ 0.</param>
+        /// <param name="p">The probability (p) of a trial resulting in success. Range: 0 ≤ p ≤ 1.</param>
+        /// <returns>the probability mass at location <paramref name="k"/>.</returns>
+        public static double PMF(double r, double p, int k)
+        {
+            return Math.Exp(PMFLn(r, p, k));
+        }
+
+        /// <summary>
+        /// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
+        /// </summary>
+        /// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
+        /// <param name="r">The number of failures (r) until the experiment stopped. Range: r ≥ 0.</param>
+        /// <param name="p">The probability (p) of a trial resulting in success. Range: 0 ≤ p ≤ 1.</param>
+        /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
+        public static double PMFLn(double r, double p, int k)
+        {
+            if (!(r >= 0.0 && p >= 0.0 && p <= 1.0)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+
+            return SpecialFunctions.GammaLn(r + k)
+                   - SpecialFunctions.GammaLn(r)
+                   - SpecialFunctions.GammaLn(k + 1.0)
+                   + (r*Math.Log(p))
+                   + (k*Math.Log(1.0 - p));
+        }
+
+        /// <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="r">The number of failures (r) until the experiment stopped. Range: r ≥ 0.</param>
+        /// <param name="p">The probability (p) of a trial resulting in success. Range: 0 ≤ p ≤ 1.</param>
+        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
+        /// <seealso cref="CumulativeDistribution"/>
+        public static double CDF(double r, double p, double x)
+        {
+            if (!(r >= 0.0 && p >= 0.0 && p <= 1.0)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+
+            return 1 - SpecialFunctions.BetaRegularized(x + 1, r, 1 - p);
         }
 
         /// <summary>

src/Numerics/Distributions/Poisson.cs

@@ -220,6 +220,43 @@ namespace MathNet.Numerics.Distributions
             return 1.0 - SpecialFunctions.GammaLowerRegularized(x + 1, _lambda);
         }
 
+        /// <summary>
+        /// Computes the probability mass (PMF) at k, i.e. P(X = k).
+        /// </summary>
+        /// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
+        /// <param name="lambda">The lambda (λ) parameter of the Poisson distribution. Range: λ > 0.</param>
+        /// <returns>the probability mass at location <paramref name="k"/>.</returns>
+        public static double PMF(double lambda, int k)
+        {
+            if (!(lambda > 0.0)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+            return Math.Exp(-lambda + (k*Math.Log(lambda)) - SpecialFunctions.FactorialLn(k));
+        }
+
+        /// <summary>
+        /// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
+        /// </summary>
+        /// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
+        /// <param name="lambda">The lambda (λ) parameter of the Poisson distribution. Range: λ > 0.</param>
+        /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
+        public static double PMFLn(double lambda, int k)
+        {
+            if (!(lambda > 0.0)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+            return -lambda + (k*Math.Log(lambda)) - SpecialFunctions.FactorialLn(k);
+        }
+
+        /// <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="lambda">The lambda (λ) parameter of the Poisson distribution. Range: λ > 0.</param>
+        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
+        /// <seealso cref="CumulativeDistribution"/>
+        public static double CDF(double lambda, double x)
+        {
+            if (!(lambda > 0.0)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+            return 1.0 - SpecialFunctions.GammaLowerRegularized(x + 1, lambda);
+        }
+
         /// <summary>
         /// Generates one sample from the Poisson distribution.
         /// </summary>

src/Numerics/Distributions/Zipf.cs

@@ -259,14 +259,51 @@ namespace MathNet.Numerics.Distributions
         /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
         public double CumulativeDistribution(double x)
         {
-            if (x < 1)
-            {
-                return 0.0;
-            }
-
+            if (x < 1) return 0.0;
             return SpecialFunctions.GeneralHarmonic((int)x, _s)/SpecialFunctions.GeneralHarmonic(_n, _s);
         }
 
+        /// <summary>
+        /// Computes the probability mass (PMF) at k, i.e. P(X = k).
+        /// </summary>
+        /// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
+        /// <param name="s">The s parameter of the distribution.</param>
+        /// <param name="n">The n parameter of the distribution.</param>
+        /// <returns>the probability mass at location <paramref name="k"/>.</returns>
+        public static double PMF(double s, int n, int k)
+        {
+            if (!(n > 0 && s > 0.0)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+            return (1.0/Math.Pow(k, s))/SpecialFunctions.GeneralHarmonic(n, s);
+        }
+
+        /// <summary>
+        /// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
+        /// </summary>
+        /// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
+        /// <param name="s">The s parameter of the distribution.</param>
+        /// <param name="n">The n parameter of the distribution.</param>
+        /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
+        public static double PMFLn(double s, int n, int k)
+        {
+            if (!(n > 0 && s > 0.0)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+            return Math.Log(PMF(s, n, k));
+        }
+
+        /// <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="s">The s parameter of the distribution.</param>
+        /// <param name="n">The n parameter of the distribution.</param>
+        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
+        /// <seealso cref="CumulativeDistribution"/>
+        public static double CDF(double s, int n, double x)
+        {
+            if (!(n > 0 && s > 0.0)) throw new ArgumentException(Resources.InvalidDistributionParameters);
+            if (x < 1) return 0.0;
+            return SpecialFunctions.GeneralHarmonic((int)x, s)/SpecialFunctions.GeneralHarmonic(n, s);
+        }
+
         /// <summary>
         /// Generates a sample from the Zipf distribution without doing parameter checking.
         /// </summary>

src/UnitTests/DistributionTests/Discrete/CategoricalTests.cs

@@ -165,7 +165,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Discrete
         [Test]
         public void CanSampleStatic()
         {
-            Categorical.SampleWithProbabilityMass(new Random(0), _largeP);
+            Categorical.Sample(new Random(0), _largeP);
         }
 
         /// <summary>
@@ -174,7 +174,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Discrete
         [Test]
         public void FailSampleStatic()
         {
-            Assert.That(() => Categorical.SampleWithProbabilityMass(new Random(0), _badP), Throws.ArgumentException);
+            Assert.That(() => Categorical.Sample(new Random(0), _badP), Throws.ArgumentException);
         }
 
         /// <summary>

src/UnitTests/DistributionTests/Discrete/HypergeometricTests.cs

@@ -280,7 +280,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Discrete
         public void ValidateProbability(int population, int success, int draws, int x)
         {
             var d = new Hypergeometric(population, success, draws);
-            Assert.AreEqual(SpecialFunctions.Binomial(success, x)*SpecialFunctions.Binomial(population - success, draws - x)/SpecialFunctions.Binomial(population, draws), d.Probability(x));
+            Assert.That(d.Probability(x), Is.EqualTo(SpecialFunctions.Binomial(success, x)*SpecialFunctions.Binomial(population - success, draws - x)/SpecialFunctions.Binomial(population, draws)));
         }
 
         /// <summary>
@@ -302,7 +302,7 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Discrete
         public void ValidateProbabilityLn(int population, int success, int draws, int x)
         {
             var d = new Hypergeometric(population, success, draws);
-            Assert.AreEqual(Math.Log(d.Probability(x)), d.ProbabilityLn(x));
+            Assert.That(d.ProbabilityLn(x), Is.EqualTo(Math.Log(d.Probability(x))).Within(1e-14));
         }
 
         /// <summary>