// <copyright file="NegativeBinomial.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>
|
|
using System;
|
using System.Collections.Generic;
|
using IStation.Numerics.Random;
|
|
namespace IStation.Numerics.Distributions
|
{
|
/// <summary>
|
/// Discrete Univariate Negative Binomial distribution.
|
/// The negative binomial is a distribution over the natural numbers with two parameters r, p. For the special
|
/// case that r is an integer one can interpret the distribution as the number of failures before the r'th success
|
/// when the probability of success is p.
|
/// <a href="http://en.wikipedia.org/wiki/Negative_binomial_distribution">Wikipedia - NegativeBinomial distribution</a>.
|
/// </summary>
|
public class NegativeBinomial : IDiscreteDistribution
|
{
|
System.Random _random;
|
|
readonly double _r;
|
readonly double _p;
|
|
/// <summary>
|
/// Initializes a new instance of the <see cref="NegativeBinomial"/> class.
|
/// </summary>
|
/// <param name="r">The number of successes (r) required to stop the experiment. Range: r ≥ 0.</param>
|
/// <param name="p">The probability (p) of a trial resulting in success. Range: 0 ≤ p ≤ 1.</param>
|
public NegativeBinomial(double r, double p)
|
{
|
if (!IsValidParameterSet(r, p))
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
_random = SystemRandomSource.Default;
|
_p = p;
|
_r = r;
|
}
|
|
/// <summary>
|
/// Initializes a new instance of the <see cref="NegativeBinomial"/> class.
|
/// </summary>
|
/// <param name="r">The number of successes (r) required to stop the experiment. Range: r ≥ 0.</param>
|
/// <param name="p">The probability (p) of a trial resulting in success. Range: 0 ≤ p ≤ 1.</param>
|
/// <param name="randomSource">The random number generator which is used to draw random samples.</param>
|
public NegativeBinomial(double r, double p, System.Random randomSource)
|
{
|
if (!IsValidParameterSet(r, p))
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
_random = randomSource ?? SystemRandomSource.Default;
|
_p = p;
|
_r = r;
|
}
|
|
/// <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 $"NegativeBinomial(R = {_r}, P = {_p})";
|
}
|
|
/// <summary>
|
/// Tests whether the provided values are valid parameters for this distribution.
|
/// </summary>
|
/// <param name="r">The number of successes (r) required to stop the experiment. Range: r ≥ 0.</param>
|
/// <param name="p">The probability (p) of a trial resulting in success. Range: 0 ≤ p ≤ 1.</param>
|
public static bool IsValidParameterSet(double r, double p)
|
{
|
return r >= 0.0 && p >= 0.0 && p <= 1.0;
|
}
|
|
/// <summary>
|
/// Gets the number of successes. Range: r ≥ 0.
|
/// </summary>
|
public double R => _r;
|
|
/// <summary>
|
/// Gets the probability of success. Range: 0 ≤ p ≤ 1.
|
/// </summary>
|
public double P => _p;
|
|
/// <summary>
|
/// Gets or sets the random number generator which is used to draw random samples.
|
/// </summary>
|
public System.Random RandomSource
|
{
|
get => _random;
|
set => _random = value ?? SystemRandomSource.Default;
|
}
|
|
/// <summary>
|
/// Gets the mean of the distribution.
|
/// </summary>
|
public double Mean => _r*(1.0 - _p)/_p;
|
|
/// <summary>
|
/// Gets the variance of the distribution.
|
/// </summary>
|
public double Variance => _r*(1.0 - _p)/(_p*_p);
|
|
/// <summary>
|
/// Gets the standard deviation of the distribution.
|
/// </summary>
|
public double StdDev => Math.Sqrt(_r*(1.0 - _p))/_p;
|
|
/// <summary>
|
/// Gets the entropy of the distribution.
|
/// </summary>
|
public double Entropy => throw new NotSupportedException();
|
|
/// <summary>
|
/// Gets the skewness of the distribution.
|
/// </summary>
|
public double Skewness => (2.0 - _p)/Math.Sqrt(_r*(1.0 - _p));
|
|
/// <summary>
|
/// Gets the mode of the distribution
|
/// </summary>
|
public int Mode => _r > 1.0 ? (int)Math.Floor((_r - 1.0)*(1.0 - _p)/_p) : 0;
|
|
/// <summary>
|
/// Gets the median of the distribution.
|
/// </summary>
|
public double 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(_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>
|
/// <returns>the log probability mass at location <paramref name="k"/>.</returns>
|
public double ProbabilityLn(int k)
|
{
|
return PMFLn(_r, _p, 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(_r, _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 successes (r) required to stop the experiment. 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 successes (r) required to stop the experiment. 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("Invalid parametrization for the distribution.");
|
}
|
|
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 successes (r) required to stop the experiment. 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("Invalid parametrization for the distribution.");
|
}
|
|
return 1 - SpecialFunctions.BetaRegularized(x + 1, r, 1 - p);
|
}
|
|
/// <summary>
|
/// Samples a negative binomial distributed random variable.
|
/// </summary>
|
/// <param name="rnd">The random number generator to use.</param>
|
/// <param name="r">The number of successes (r) required to stop the experiment. Range: r ≥ 0.</param>
|
/// <param name="p">The probability (p) of a trial resulting in success. Range: 0 ≤ p ≤ 1.</param>
|
/// <returns>a sample from the distribution.</returns>
|
static int SampleUnchecked(System.Random rnd, double r, double p)
|
{
|
var lambda = Gamma.SampleUnchecked(rnd, r, p);
|
var c = Math.Exp(-lambda);
|
var p1 = 1.0;
|
var k = 0;
|
do
|
{
|
k = k + 1;
|
p1 = p1*rnd.NextDouble();
|
}
|
while (p1 >= c);
|
return k - 1;
|
}
|
|
static void SamplesUnchecked(System.Random rnd, int[] values, double r, double p)
|
{
|
for (int i = 0; i < values.Length; i++)
|
{
|
values[i] = SampleUnchecked(rnd, r, p);
|
}
|
}
|
|
static IEnumerable<int> SamplesUnchecked(System.Random rnd, double r, double p)
|
{
|
while (true)
|
{
|
yield return SampleUnchecked(rnd, r, p);
|
}
|
}
|
|
/// <summary>
|
/// Samples a <c>NegativeBinomial</c> distributed random variable.
|
/// </summary>
|
/// <returns>a sample from the distribution.</returns>
|
public int Sample()
|
{
|
return SampleUnchecked(_random, _r, _p);
|
}
|
|
/// <summary>
|
/// Fills an array with samples generated from the distribution.
|
/// </summary>
|
public void Samples(int[] values)
|
{
|
SamplesUnchecked(_random, values, _r, _p);
|
}
|
|
/// <summary>
|
/// Samples an array of <c>NegativeBinomial</c> distributed random variables.
|
/// </summary>
|
/// <returns>a sequence of samples from the distribution.</returns>
|
public IEnumerable<int> Samples()
|
{
|
return SamplesUnchecked(_random, _r, _p);
|
}
|
|
/// <summary>
|
/// Samples a random variable.
|
/// </summary>
|
/// <param name="rnd">The random number generator to use.</param>
|
/// <param name="r">The number of successes (r) required to stop the experiment. Range: r ≥ 0.</param>
|
/// <param name="p">The probability (p) of a trial resulting in success. Range: 0 ≤ p ≤ 1.</param>
|
public static int Sample(System.Random rnd, double r, double p)
|
{
|
if (!(r >= 0.0 && p >= 0.0 && p <= 1.0))
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
return SampleUnchecked(rnd, r, p);
|
}
|
|
/// <summary>
|
/// Samples a sequence of this random variable.
|
/// </summary>
|
/// <param name="rnd">The random number generator to use.</param>
|
/// <param name="r">The number of successes (r) required to stop the experiment. Range: r ≥ 0.</param>
|
/// <param name="p">The probability (p) of a trial resulting in success. Range: 0 ≤ p ≤ 1.</param>
|
public static IEnumerable<int> Samples(System.Random rnd, double r, double p)
|
{
|
if (!(r >= 0.0 && p >= 0.0 && p <= 1.0))
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
return SamplesUnchecked(rnd, r, p);
|
}
|
|
/// <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="r">The number of successes (r) required to stop the experiment. Range: r ≥ 0.</param>
|
/// <param name="p">The probability (p) of a trial resulting in success. Range: 0 ≤ p ≤ 1.</param>
|
public static void Samples(System.Random rnd, int[] values, double r, double p)
|
{
|
if (!(r >= 0.0 && p >= 0.0 && p <= 1.0))
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
SamplesUnchecked(rnd, values, r, p);
|
}
|
|
/// <summary>
|
/// Samples a random variable.
|
/// </summary>
|
/// <param name="r">The number of successes (r) required to stop the experiment. Range: r ≥ 0.</param>
|
/// <param name="p">The probability (p) of a trial resulting in success. Range: 0 ≤ p ≤ 1.</param>
|
public static int Sample(double r, double p)
|
{
|
if (!(r >= 0.0 && p >= 0.0 && p <= 1.0))
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
return SampleUnchecked(SystemRandomSource.Default, r, p);
|
}
|
|
/// <summary>
|
/// Samples a sequence of this random variable.
|
/// </summary>
|
/// <param name="r">The number of successes (r) required to stop the experiment. Range: r ≥ 0.</param>
|
/// <param name="p">The probability (p) of a trial resulting in success. Range: 0 ≤ p ≤ 1.</param>
|
public static IEnumerable<int> Samples(double r, double p)
|
{
|
if (!(r >= 0.0 && p >= 0.0 && p <= 1.0))
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
return SamplesUnchecked(SystemRandomSource.Default, r, p);
|
}
|
|
/// <summary>
|
/// Fills an array with samples generated from the distribution.
|
/// </summary>
|
/// <param name="values">The array to fill with the samples.</param>
|
/// <param name="r">The number of successes (r) required to stop the experiment. Range: r ≥ 0.</param>
|
/// <param name="p">The probability (p) of a trial resulting in success. Range: 0 ≤ p ≤ 1.</param>
|
public static void Samples(int[] values, double r, double p)
|
{
|
if (!(r >= 0.0 && p >= 0.0 && p <= 1.0))
|
{
|
throw new ArgumentException("Invalid parametrization for the distribution.");
|
}
|
|
SamplesUnchecked(SystemRandomSource.Default, values, r, p);
|
}
|
}
|
}
|
