Beta-Binomial distribution, Generalized Hypergeometric Function, Rising and Falling Factorials.

6 years ago · 5cef0b7ea2
4 changed files with 563 additions and 1 deletions
--- a/.gitignore
+++ b/.gitignore
@ -77,3 +77,4 @@ docs/content/Contributing.md
 docs/content/Contributors.md
 docs/content/ReleaseNotes.md
 docs/content/ReleaseNotes-*.md
+/build.fsx.lock
--- a/src/Numerics/Distributions/BetaBinomial.cs
+++ b/src/Numerics/Distributions/BetaBinomial.cs
@ -0,0 +1,416 @@
+// <copyright file="BetaBinomial.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+//
+// 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
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+//
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+// <contribution>
+//    Andrew J. Willshire
+// </contribution>
+
+
+using System;
+using System.Collections.Generic;
+using MathNet.Numerics.Properties;
+using MathNet.Numerics.Random;
+
+namespace MathNet.Numerics.Distributions
+{
+    /// <summary>
+    /// Discrete Univariate Beta-Binomial distribution.
+    /// The beta-binomial distribution is a family of discrete probability distributions on a finite support of non-negative integers arising
+    /// when the probability of success in each of a fixed or known number of Bernoulli trials is either unknown or random.
+    /// The beta-binomial distribution is the binomial distribution in which the probability of success at each of n trials is not fixed but randomly drawn from a beta distribution.
+    /// It is frequently used in Bayesian statistics, empirical Bayes methods and classical statistics to capture overdispersion in binomial type distributed data.
+    /// <a href="https://en.wikipedia.org/wiki/Beta-binomial_distribution">Wikipedia - Beta-Binomial distribution</a>.
+    /// </summary>
+    public class BetaBinomial : IDiscreteDistribution
+    {
+        System.Random _random;
+
+        readonly int _n;
+        readonly double _a;
+        readonly double _b;
+
+        /// <summary>
+        /// Initializes a new instance of the <see cref="BetaBinomial"/> class.
+        /// </summary>
+        /// <param name="n">The number of Bernoulli trials n - n is a positive integer </param>
+        /// <param name="a">Shape parameter alpha of the Beta distribution. Range: a > 0.</param>
+        /// <param name="b">Shape parameter beta of the Beta distribution. Range: b > 0.</param>
+        public BetaBinomial(int n, double a, double b)
+        {
+            if (!IsValidParameterSet(n, a, b))
+            {
+                throw new ArgumentException(Resources.InvalidDistributionParameters);
+            }
+
+            _random = SystemRandomSource.Default;
+            _n = n;
+            _a = a;
+            _b = b;
+        }
+
+        /// <summary>
+        /// Initializes a new instance of the <see cref="BetaBinomial"/> class.
+        /// </summary>
+        /// <param name="n">The number of Bernoulli trials n - n is a positive integer </param>
+        /// <param name="a">Shape parameter alpha of the Beta distribution. Range: a > 0.</param>
+        /// <param name="b">Shape parameter beta of the Beta distribution. Range: b > 0.</param>
+        /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
+        public BetaBinomial(int n, double a, double b, System.Random randomSource)
+        {
+            if (!IsValidParameterSet(n,a,b))
+            {
+                throw new ArgumentException(Resources.InvalidDistributionParameters);
+            }
+
+            _random = randomSource ?? SystemRandomSource.Default;
+            _n = n;
+            _a = a;
+            _b = b;
+        }
+
+        /// <summary>
+        /// Returns a <see cref="System.String"/> that represents this instance.
+        /// </summary>
+        /// <returns>
+        /// A <see cref="System.String"/> that represents this instance.
+        /// </returns>
+        public override string ToString()
+        {
+            return $"BetaBinomial(n = {_n}, a = {_a}, b = {_b})";
+        }
+
+        /// <summary>
+        /// Tests whether the provided values are valid parameters for this distribution.
+        /// </summary>
+        /// <param name="n">The number of Bernoulli trials n - n is a positive integer </param>
+        /// <param name="a">Shape parameter alpha of the Beta distribution. Range: a > 0.</param>
+        /// <param name="b">Shape parameter beta of the Beta distribution. Range: b > 0.</param>
+        public static bool IsValidParameterSet(int n, double a, double b)
+        {
+            return n >= 1.0 && a > 0.0 && b > 0.0;
+        }
+
+        /// <summary>
+        /// Tests whether the provided values are valid parameters for this distribution.
+        /// </summary>
+        /// <param name="n">The number of Bernoulli trials n - n is a positive integer </param>
+        /// <param name="a">Shape parameter alpha of the Beta distribution. Range: a > 0.</param>
+        /// <param name="b">Shape parameter beta of the Beta distribution. Range: b > 0.</param>
+        /// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
+        public static bool IsValidParameterSet(int n, double a, double b, int k)
+        {
+            return n >= 1.0 && a > 0.0 && b > 0.0 && k >=0 && k <=n;
+        }
+
+
+        public int N => _n;
+        public double A => _a;
+        public double B => _b;
+
+        public System.Random RandomSource
+        {
+            get => _random;
+            set => _random = value ?? SystemRandomSource.Default;
+        }
+        /// <summary>
+        /// Gets the mean of the distribution.
+        /// </summary>
+        double IUnivariateDistribution.Mean => (_n * _a) / (_a + _b);
+
+        /// <summary>
+        /// Gets the variance of the distribution.
+        /// </summary>
+        double IUnivariateDistribution.Variance => (_n*_a*_b*(_a+_b+_n))/(Math.Pow((_a+_b),2) * (_a+_b+1));
+
+        /// <summary>
+        /// Gets the standard deviation of the distribution.
+        /// </summary>
+        double IUnivariateDistribution.StdDev => Math.Sqrt((_n * _a * _b * (_a + _b + _n)) / (Math.Pow((_a + _b), 2) * (_a + _b + 1)));
+
+        /// <summary>
+        /// Gets the entropy of the distribution.
+        /// </summary>
+        double IUnivariateDistribution.Entropy => throw new NotSupportedException();
+
+        /// <summary>
+        /// Gets the skewness of the distribution.
+        /// </summary>
+        double IUnivariateDistribution.Skewness =>
+            (_a + _b + 2 * _n) * (_b - _a) / (_a + _b + 2) * Math.Sqrt((1 + _a + _b) / (_n * _a * _b * (_n + _a + _b)));
+
+        /// <summary>
+        /// Gets the mode of the distribution
+        /// </summary>
+        int IDiscreteDistribution.Mode => throw new NotSupportedException();
+ 
+        /// <summary>
+        /// Gets the median of the distribution.
+        /// </summary>
+        double IUnivariateDistribution.Median => throw new NotSupportedException();
+
+        /// <summary>
+        /// Gets the smallest element in the domain of the distributions which can be represented by an integer.
+        /// </summary>
+        public int Minimum => 0;
+
+        /// <summary>
+        /// Gets the largest element in the domain of the distributions which can be represented by an integer.
+        /// </summary>
+        public int Maximum => int.MaxValue;
+
+        /// <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>
+        /// <returns>the probability mass at location <paramref name="k"/>.</returns>
+        public double Probability(int k)
+        {
+            return PMF(_n, _a, _b, 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>
+        /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
+        public double ProbabilityLn(int k)
+        {
+            return PMFLn(_n, _a, _b, 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>
+        /// <returns>the cumulative distribution at location <paramref name="x"/></returns>
+        public double CumulativeDistribution(double x)
+        {
+            return CDF(_n, _a, _b, (int)Math.Floor(x));
+        }
+
+        /// <summary>
+        /// Computes the probability mass (PMF) at k, i.e. P(X = k).
+        /// </summary>
+        /// <param name="n">The number of Bernoulli trials n - n is a positive integer </param>
+        /// <param name="a">Shape parameter alpha of the Beta distribution. Range: a > 0.</param>
+        /// <param name="b">Shape parameter beta of the Beta distribution. Range: b > 0.</param>
+        /// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
+        /// <returns>the probability mass at location <paramref name="k"/>.</returns>
+        public static double PMF(int n, double a, double b, int k)
+        {
+            if (!IsValidParameterSet(n, a, b, k))
+            {
+                throw new ArgumentException(Resources.InvalidDistributionParameters);
+            }
+
+            if (k > n)
+            {
+                return 0.0;
+            }
+            else
+            {
+            return Math.Exp(PMFLn(n, a, b, k));
+            }
+        }
+
+        /// <summary>
+        /// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
+        /// </summary>
+        /// <param name="n">The number of Bernoulli trials n - n is a positive integer </param>
+        /// <param name="a">Shape parameter alpha of the Beta distribution. Range: a > 0.</param>
+        /// <param name="b">Shape parameter beta of the Beta distribution. Range: b > 0.</param>
+        /// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
+        /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
+        public static double PMFLn(int n, double a, double b, int k)
+        {
+            if (!IsValidParameterSet(n, a, b, k))
+            {
+                throw new ArgumentException(Resources.InvalidDistributionParameters);
+            }
+
+            return SpecialFunctions.BinomialLn((n), k)
+                + SpecialFunctions.BetaLn(k + a, n - k + b)
+                - SpecialFunctions.BetaLn(a, b);
+        }
+
+        /// <summary>
+        /// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
+        /// </summary>
+        /// <param name="n">The number of Bernoulli trials n - n is a positive integer </param>
+        /// <param name="a">Shape parameter alpha of the Beta distribution. Range: a > 0.</param>
+        /// <param name="b">Shape parameter beta of the Beta distribution. Range: b > 0.</param>
+        /// <param name="x">The location at which to compute the cumulative distribution function.</param>
+        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
+        /// <seealso cref="CumulativeDistribution"/>
+        public static double CDF(int n, double a, double b, int x)
+        {
+            if (!IsValidParameterSet(n,a,b,x))
+            {
+                throw new ArgumentException(Resources.InvalidDistributionParameters);
+            }
+
+            double accumulator = 0;
+
+            for (int i = 0; i<=x; i++)
+            {
+                accumulator += PMF(n, a, b, i);
+            }
+
+            return accumulator;
+        }
+
+        /// <summary>
+        /// Samples BetaBinomial distributed random variables by sampling a Beta distribution then passing to a Binomial distribution.
+        /// </summary>
+        /// <param name="rnd">The random number generator to use.</param>
+        /// <param name="a">The α shape parameter of the Beta distribution. Range: α ≥ 0.</param>
+        /// <param name="b">The β shape parameter of the Beta distribution. Range: β ≥ 0.</param>
+        /// <param name="n">The number of trials (n). Range: n ≥ 0.</param>
+        /// <returns>a random number from the BetaBinomial distribution.</returns>
+        static int SampleUnchecked(System.Random rnd, int n, double a, double b)
+        {
+            var p = Beta.SampleUnchecked(rnd, a, b);
+            var x = Binomial.SampleUnchecked(rnd, p, n);
+            return x;
+        }
+
+        static void SamplesUnchecked(System.Random rnd, int[] values, int n, double a, double b)
+        {
+            for (int i = 0; i < values.Length; i++)
+            {
+                values[i] = SampleUnchecked(rnd, n, a, b);
+            }
+        }
+
+        static IEnumerable<int> SamplesUnchecked(System.Random rnd, int n, double a, double b)
+        {
+            while (true)
+            {
+                yield return SampleUnchecked(rnd, n, a, b);
+            }
+        }
+
+
+        /// <summary>
+        /// Samples a <c>BetaBinomial</c> distributed random variable.
+        /// </summary>
+        /// <returns>a sample from the distribution.</returns>
+
+        public int Sample()
+        {
+            return SampleUnchecked(_random, _n, _a, _b);
+        }
+
+        /// <summary>
+        /// Fills an array with samples generated from the distribution.
+        /// </summary>
+       public void Samples(int[] values)
+        {
+            SamplesUnchecked(_random, values, _n, _a, _b);
+        }
+
+        /// <summary>
+        /// Samples an array of <c>BetaBinomial</c> distributed random variables.
+        /// </summary>
+        /// <returns>a sequence of samples from the distribution.</returns>
+        public IEnumerable<int> Samples()
+        {
+            return SamplesUnchecked(_random, _n, _a, _b);
+        }
+
+        /// <summary>
+        /// Samples a <c>BetaBinomial</c> distributed random variable.
+        /// </summary>
+        /// <param name="rnd">The random number generator to use.</param>
+        /// <param name="a">The α shape parameter of the Beta distribution. Range: α ≥ 0.</param>
+        /// <param name="b">The β shape parameter of the Beta distribution. Range: β ≥ 0.</param>
+        /// <param name="n">The number of trials (n). Range: n ≥ 0.</param>
+        /// <returns>a sample from the distribution.</returns>
+
+        public int Sample(System.Random rnd, int n, double a, double b)
+        {
+            if (!IsValidParameterSet(n,a,b))
+            {
+                throw new ArgumentException(Resources.InvalidDistributionParameters);
+            }
+            return SampleUnchecked(rnd, n, a, b);
+        }
+
+        /// <summary>
+        /// Fills an array with samples generated from the distribution.
+        /// </summary>
+        /// <param name="rnd">The random number generator to use.</param>
+        /// <param name="values">The array to fill with the samples.</param>
+        /// <param name="a">The α shape parameter of the Beta distribution. Range: α ≥ 0.</param>
+        /// <param name="b">The β shape parameter of the Beta distribution. Range: β ≥ 0.</param>
+        /// <param name="n">The number of trials (n). Range: n ≥ 0.</param>
+        public void Samples(System.Random rnd, int[] values, int n, double a, double b)
+        {
+            if (!IsValidParameterSet(n, a, b))
+            {
+                throw new ArgumentException(Resources.InvalidDistributionParameters);
+            }
+
+            SamplesUnchecked(rnd, values, n, a, b);
+        }
+
+        /// <summary>
+        /// Samples an array of <c>BetaBinomial</c> distributed random variables.
+        /// </summary>
+        /// <param name="a">The α shape parameter of the Beta distribution. Range: α ≥ 0.</param>
+        /// <param name="b">The β shape parameter of the Beta distribution. Range: β ≥ 0.</param>
+        /// <param name="n">The number of trials (n). Range: n ≥ 0.</param>
+        /// <returns>a sequence of samples from the distribution.</returns>
+        public IEnumerable<int> Samples(int n, double a, double b)
+        {
+            if (!IsValidParameterSet(n, a, b))
+            {
+                throw new ArgumentException(Resources.InvalidDistributionParameters);
+            }
+            return SamplesUnchecked(_random, n, a, b);
+        }
+
+        /// <summary>
+        /// Fills an array with samples generated from the distribution.
+        /// </summary>
+        /// <param name="values">The array to fill with the samples.</param>
+        /// <param name="a">The α shape parameter of the Beta distribution. Range: α ≥ 0.</param>
+        /// <param name="b">The β shape parameter of the Beta distribution. Range: β ≥ 0.</param>
+        /// <param name="n">The number of trials (n). Range: n ≥ 0.</param>
+        public void Samples(int[] values, int n, double a, double b)
+        {
+            if (!IsValidParameterSet(n, a, b))
+            {
+                throw new ArgumentException(Resources.InvalidDistributionParameters);
+            }
+
+            SamplesUnchecked(_random, values, n, a, b);
+        }
+    }
+}
--- a/src/Numerics/Distributions/Binomial.cs
+++ b/src/Numerics/Distributions/Binomial.cs
@ -359,7 +359,7 @@ namespace MathNet.Numerics.Distributions
        /// <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 number of successful trials.</returns>
-        static int SampleUnchecked(System.Random rnd, double p, int n)
+        internal static int SampleUnchecked(System.Random rnd, double p, int n)
        {
            var k = 0;
            for (var i = 0; i < n; i++)
--- a/src/Numerics/SpecialFunctions/GeneralizedHyperGeometric.cs
+++ b/src/Numerics/SpecialFunctions/GeneralizedHyperGeometric.cs
@ -0,0 +1,145 @@
+// <copyright file="GeneralizedHyperGeometric.cs" company="Math.NET">
+// Math.NET Numerics, part of the Math.NET Project
+// http://numerics.mathdotnet.com
+// http://github.com/mathnet/mathnet-numerics
+//
+// Copyright (c) 2009-2010 Math.NET
+//
+// Permission is hereby granted, free of charge, to any person
+// obtaining a copy of this software and associated documentation
+// files (the "Software"), to deal in the Software without
+// restriction, including without limitation the rights to use,
+// copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following
+// conditions:
+//
+// The above copyright notice and this permission notice shall be
+// included in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+// OTHER DEALINGS IN THE SOFTWARE.
+// </copyright>
+
+// <contribution>
+//    Andrew J. Willshire
+// </contribution>
+
+using System;
+using System.Linq;
+
+namespace MathNet.Numerics
+{
+    public static partial class SpecialFunctions
+    {
+
+        //Rising and falling factorials - reference here:
+        //https://en.wikipedia.org/wiki/Falling_and_rising_factorials
+
+
+        /// <summary>
+        /// Computes the Rising Factorial (Pochhammer function)  x -> (x)n, n>= 0. see: https://en.wikipedia.org/wiki/Falling_and_rising_factorials
+        /// </summary>
+        /// <returns>The real value of the Rising Factorial for x and n</returns>
+
+        public static double RisingFactorial(double x, int n)
+        {
+                double accumulator = 1.0;
+
+                for (int k = 0; k < n; k++)
+                {
+                    accumulator *= (x + k);
+                }
+                return accumulator;
+            }
+
+        /// <summary>
+        /// Computes the Falling Factorial (Pochhammer function)  x -> x(n), n>= 0. see: https://en.wikipedia.org/wiki/Falling_and_rising_factorials
+        /// </summary>
+        /// <returns>The real value of the Falling Factorial for x and n</returns>
+        public static double FallingFactorial(double x, int n)
+        {
+                double accumulator = 1.0;
+
+                for (int k = 0; k < n; k++)
+                {
+                    accumulator *= (x - k);
+                }
+                return accumulator;
+        }
+        //
+
+        /// <summary>
+        /// A generalized hypergeometric series is a power series in which the ratio of successive coefficients indexed by n is a rational function of n.
+        /// This is the most common pFq(a1, ..., ap; b1,...,bq; z) representation
+        /// see: https://en.wikipedia.org/wiki/Generalized_hypergeometric_function
+        /// </summary>
+        /// <param name="a">The list of coefficients in the numerator</param>
+        /// <param name="b">The list of coefficients in the denominator</param>
+        /// <param name="z">The variable in the power series</param>
+        /// <returns>The value of the Generalized HyperGeometric Function.</returns>
+        public static double GeneralizedHypergeometric(double[] a, double[] b, int z)
+        {
+            const double epsilon = 0.000000000000001;
+
+            double cumulatives = 0.0;
+            double currentIncrement;
+            int n = 0;
+
+            do
+            {
+                currentIncrement = HGIncrement(a, b, z, n);
+                cumulatives += currentIncrement;
+                n += 1;
+            }
+            while (Math.Abs(currentIncrement) > epsilon && Math.Abs(currentIncrement) > 0 && currentIncrement.IsFinite());
+
+            return cumulatives;
+        }
+
+        //Calculate each iteration of the function
+        private static double HGIncrement(double[] a, double[] b, int z, int currentN)
+        {
+            double incrementAs = 1.0;
+            double incrementBs = 1.0;
+
+            double[] incrementAArray = new double[a.Length];
+            double[] incrementBArray = new double[b.Length];
+
+            for (int p = 0; p < a.Length; p++)
+            {
+                incrementAs *= RisingFactorial(a[p], currentN);
+                incrementAArray[p] = RisingFactorial(a[p], currentN);
+            }
+
+            for (int q = 0; q < b.Length; q++)
+            {
+                incrementBs *= RisingFactorial(b[q], currentN);
+                incrementBArray[q] = RisingFactorial(b[q], currentN);
+            }
+
+            double numZeros = (from x in incrementAArray where x == 0 select x).Count();
+            double numPoles = (from x in incrementBArray where x == 0 select x).Count();
+
+            if (numZeros > 0 && numZeros >= numPoles)
+            {
+                return 0.0;
+            }
+            else if (numPoles > 0 && numPoles > numZeros)
+            {
+                return double.PositiveInfinity;
+            }
+            else
+            {
+            return incrementAs / incrementBs * Math.Pow(z, currentN) / Factorial(currentN);
+            }
+        }
+
+    }
+}