// <copyright file="Hypergeometric.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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//
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// Copyright (c) 2009-2014 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System;
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using System.Collections.Generic;
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using IStation.Numerics.Random;
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namespace IStation.Numerics.Distributions
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{
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/// <summary>
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/// Discrete Univariate Hypergeometric distribution.
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/// This distribution is a discrete probability distribution that describes the number of successes in a sequence
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/// of n draws from a finite population without replacement, just as the binomial distribution
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/// describes the number of successes for draws with replacement
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/// <a href="http://en.wikipedia.org/wiki/Hypergeometric_distribution">Wikipedia - Hypergeometric distribution</a>.
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/// </summary>
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public class Hypergeometric : IDiscreteDistribution
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{
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System.Random _random;
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readonly int _population;
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readonly int _success;
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readonly int _draws;
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/// <summary>
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/// Initializes a new instance of the Hypergeometric class.
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/// </summary>
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/// <param name="population">The size of the population (N).</param>
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/// <param name="success">The number successes within the population (K, M).</param>
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/// <param name="draws">The number of draws without replacement (n).</param>
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public Hypergeometric(int population, int success, int draws)
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{
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if (!IsValidParameterSet(population, success, draws))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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_random = SystemRandomSource.Default;
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_population = population;
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_success = success;
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_draws = draws;
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}
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/// <summary>
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/// Initializes a new instance of the Hypergeometric class.
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/// </summary>
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/// <param name="population">The size of the population (N).</param>
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/// <param name="success">The number successes within the population (K, M).</param>
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/// <param name="draws">The number of draws without replacement (n).</param>
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/// <param name="randomSource">The random number generator which is used to draw random samples.</param>
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public Hypergeometric(int population, int success, int draws, System.Random randomSource)
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{
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if (!IsValidParameterSet(population, success, draws))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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_random = randomSource ?? SystemRandomSource.Default;
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_population = population;
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_success = success;
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_draws = draws;
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}
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/// <summary>
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/// Returns a <see cref="System.String"/> that represents this instance.
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/// </summary>
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/// <returns>
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/// A <see cref="System.String"/> that represents this instance.
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/// </returns>
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public override string ToString()
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{
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return $"Hypergeometric(N = {_population}, M = {_success}, n = {_draws})";
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}
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/// <summary>
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/// Tests whether the provided values are valid parameters for this distribution.
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/// </summary>
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/// <param name="population">The size of the population (N).</param>
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/// <param name="success">The number successes within the population (K, M).</param>
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/// <param name="draws">The number of draws without replacement (n).</param>
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public static bool IsValidParameterSet(int population, int success, int draws)
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{
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return population >= 0 && success >= 0 && draws >= 0 && success <= population && draws <= population;
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}
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/// <summary>
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/// Gets or sets the random number generator which is used to draw random samples.
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/// </summary>
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public System.Random RandomSource
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{
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get => _random;
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set => _random = value ?? SystemRandomSource.Default;
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}
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/// <summary>
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/// Gets the size of the population (N).
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/// </summary>
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public int Population => _population;
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/// <summary>
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/// Gets the number of draws without replacement (n).
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/// </summary>
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public int Draws => _draws;
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/// <summary>
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/// Gets the number successes within the population (K, M).
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/// </summary>
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public int Success => _success;
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/// <summary>
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/// Gets the mean of the distribution.
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/// </summary>
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public double Mean => (double)_success*_draws/_population;
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/// <summary>
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/// Gets the variance of the distribution.
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/// </summary>
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public double Variance => _draws*_success*(_population - _draws)*(_population - _success)/(_population*_population*(_population - 1.0));
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/// <summary>
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/// Gets the standard deviation of the distribution.
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/// </summary>
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public double StdDev => Math.Sqrt(Variance);
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/// <summary>
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/// Gets the entropy of the distribution.
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/// </summary>
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public double Entropy => throw new NotSupportedException();
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/// <summary>
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/// Gets the skewness of the distribution.
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/// </summary>
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public double Skewness => (Math.Sqrt(_population - 1.0)*(_population - (2*_draws))*(_population - (2*_success)))/(Math.Sqrt(_draws*_success*(_population - _success)*(_population - _draws))*(_population - 2.0));
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/// <summary>
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/// Gets the mode of the distribution.
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/// </summary>
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public int Mode => (_draws + 1)*(_success + 1)/(_population + 2);
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/// <summary>
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/// Gets the median of the distribution.
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/// </summary>
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public double Median => throw new NotSupportedException();
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/// <summary>
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/// Gets the minimum of the distribution.
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/// </summary>
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public int Minimum => Math.Max(0, _draws + _success - _population);
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/// <summary>
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/// Gets the maximum of the distribution.
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/// </summary>
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public int Maximum => Math.Min(_success, _draws);
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/// <summary>
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/// Computes the probability mass (PMF) at k, i.e. P(X = k).
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/// </summary>
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/// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
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/// <returns>the probability mass at location <paramref name="k"/>.</returns>
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public double Probability(int k)
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{
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return SpecialFunctions.Binomial(_success, k)*SpecialFunctions.Binomial(_population - _success, _draws - k)/SpecialFunctions.Binomial(_population, _draws);
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}
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/// <summary>
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/// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
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/// </summary>
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/// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
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/// <returns>the log probability mass at location <paramref name="k"/>.</returns>
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public double ProbabilityLn(int k)
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{
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return SpecialFunctions.BinomialLn(_success, k) + SpecialFunctions.BinomialLn(_population - _success, _draws - k) - SpecialFunctions.BinomialLn(_population, _draws);
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}
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/// <summary>
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/// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
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/// </summary>
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/// <param name="x">The location at which to compute the cumulative distribution function.</param>
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/// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
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public double CumulativeDistribution(double x)
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{
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return CDF(_population, _success, _draws, x);
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}
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/// <summary>
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/// Computes the probability mass (PMF) at k, i.e. P(X = k).
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/// </summary>
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/// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
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/// <param name="population">The size of the population (N).</param>
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/// <param name="success">The number successes within the population (K, M).</param>
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/// <param name="draws">The number of draws without replacement (n).</param>
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/// <returns>the probability mass at location <paramref name="k"/>.</returns>
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public static double PMF(int population, int success, int draws, int k)
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{
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if (!(population >= 0 && success >= 0 && draws >= 0 && success <= population && draws <= population))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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return SpecialFunctions.Binomial(success, k)*SpecialFunctions.Binomial(population - success, draws - k)/SpecialFunctions.Binomial(population, draws);
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}
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/// <summary>
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/// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
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/// </summary>
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/// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
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/// <param name="population">The size of the population (N).</param>
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/// <param name="success">The number successes within the population (K, M).</param>
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/// <param name="draws">The number of draws without replacement (n).</param>
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/// <returns>the log probability mass at location <paramref name="k"/>.</returns>
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public static double PMFLn(int population, int success, int draws, int k)
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{
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if (!(population >= 0 && success >= 0 && draws >= 0 && success <= population && draws <= population))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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return SpecialFunctions.BinomialLn(success, k) + SpecialFunctions.BinomialLn(population - success, draws - k) - SpecialFunctions.BinomialLn(population, draws);
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}
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/// <summary>
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/// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
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/// </summary>
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/// <param name="x">The location at which to compute the cumulative distribution function.</param>
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/// <param name="population">The size of the population (N).</param>
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/// <param name="success">The number successes within the population (K, M).</param>
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/// <param name="draws">The number of draws without replacement (n).</param>
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/// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
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/// <seealso cref="CumulativeDistribution"/>
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public static double CDF(int population, int success, int draws, double x)
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{
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if (!(population >= 0 && success >= 0 && draws >= 0 && success <= population && draws <= population))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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if (x < Math.Max(0, draws + success - population))
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{
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return 0.0;
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}
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if (x >= Math.Min(success, draws))
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{
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return 1.0;
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}
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var k = (int)Math.Floor(x);
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var denominatorLn = SpecialFunctions.BinomialLn(population, draws);
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var sum = 0.0;
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for (var i = 0; i <= k; i++)
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{
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sum += Math.Exp(SpecialFunctions.BinomialLn(success, i) + SpecialFunctions.BinomialLn(population - success, draws - i) - denominatorLn);
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}
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return Math.Min(sum, 1.0);
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}
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/// <summary>
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/// Generates a sample from the Hypergeometric distribution without doing parameter checking.
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/// </summary>
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/// <param name="rnd">The random number generator to use.</param>
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/// <param name="population">The size of the population (N).</param>
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/// <param name="success">The number successes within the population (K, M).</param>
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/// <param name="draws">The n parameter of the distribution.</param>
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/// <returns>a random number from the Hypergeometric distribution.</returns>
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static int SampleUnchecked(System.Random rnd, int population, int success, int draws)
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{
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var x = 0;
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do
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{
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var p = (double)success/population;
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var r = rnd.NextDouble();
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if (r < p)
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{
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x++;
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success--;
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}
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population--;
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draws--;
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}
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while (0 < draws);
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return x;
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}
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static void SamplesUnchecked(System.Random rnd, int[] values, int population, int success, int draws)
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{
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for (int i = 0; i < values.Length; i++)
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{
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values[i] = SampleUnchecked(rnd, population, success, draws);
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}
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}
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static IEnumerable<int> SamplesUnchecked(System.Random rnd, int population, int success, int draws)
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{
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while (true)
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{
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yield return SampleUnchecked(rnd, population, success, draws);
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}
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}
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/// <summary>
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/// Samples a Hypergeometric distributed random variable.
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/// </summary>
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/// <returns>The number of successes in n trials.</returns>
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public int Sample()
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{
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return SampleUnchecked(_random, _population, _success, _draws);
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}
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/// <summary>
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/// Fills an array with samples generated from the distribution.
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/// </summary>
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public void Samples(int[] values)
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{
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SamplesUnchecked(_random, values, _population, _success, _draws);
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}
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/// <summary>
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/// Samples an array of Hypergeometric distributed random variables.
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/// </summary>
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/// <returns>a sequence of successes in n trials.</returns>
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public IEnumerable<int> Samples()
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{
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return SamplesUnchecked(_random, _population, _success, _draws);
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}
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/// <summary>
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/// Samples a random variable.
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/// </summary>
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/// <param name="rnd">The random number generator to use.</param>
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/// <param name="population">The size of the population (N).</param>
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/// <param name="success">The number successes within the population (K, M).</param>
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/// <param name="draws">The number of draws without replacement (n).</param>
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public static int Sample(System.Random rnd, int population, int success, int draws)
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{
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if (!(population >= 0 && success >= 0 && draws >= 0 && success <= population && draws <= population))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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return SampleUnchecked(rnd, population, success, draws);
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}
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/// <summary>
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/// Samples a sequence of this random variable.
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/// </summary>
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/// <param name="rnd">The random number generator to use.</param>
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/// <param name="population">The size of the population (N).</param>
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/// <param name="success">The number successes within the population (K, M).</param>
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/// <param name="draws">The number of draws without replacement (n).</param>
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public static IEnumerable<int> Samples(System.Random rnd, int population, int success, int draws)
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{
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if (!(population >= 0 && success >= 0 && draws >= 0 && success <= population && draws <= population))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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return SamplesUnchecked(rnd, population, success, draws);
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}
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/// <summary>
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/// Fills an array with samples generated from the distribution.
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/// </summary>
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/// <param name="rnd">The random number generator to use.</param>
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/// <param name="values">The array to fill with the samples.</param>
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/// <param name="population">The size of the population (N).</param>
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/// <param name="success">The number successes within the population (K, M).</param>
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/// <param name="draws">The number of draws without replacement (n).</param>
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public static void Samples(System.Random rnd, int[] values, int population, int success, int draws)
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{
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if (!(population >= 0 && success >= 0 && draws >= 0 && success <= population && draws <= population))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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SamplesUnchecked(rnd, values, population, success, draws);
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}
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/// <summary>
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/// Samples a random variable.
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/// </summary>
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/// <param name="population">The size of the population (N).</param>
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/// <param name="success">The number successes within the population (K, M).</param>
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/// <param name="draws">The number of draws without replacement (n).</param>
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public static int Sample(int population, int success, int draws)
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{
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if (!(population >= 0 && success >= 0 && draws >= 0 && success <= population && draws <= population))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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return SampleUnchecked(SystemRandomSource.Default, population, success, draws);
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}
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/// <summary>
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/// Samples a sequence of this random variable.
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/// </summary>
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/// <param name="population">The size of the population (N).</param>
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/// <param name="success">The number successes within the population (K, M).</param>
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/// <param name="draws">The number of draws without replacement (n).</param>
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public static IEnumerable<int> Samples(int population, int success, int draws)
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{
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if (!(population >= 0 && success >= 0 && draws >= 0 && success <= population && draws <= population))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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return SamplesUnchecked(SystemRandomSource.Default, population, success, draws);
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}
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/// <summary>
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/// Fills an array with samples generated from the distribution.
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/// </summary>
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/// <param name="values">The array to fill with the samples.</param>
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/// <param name="population">The size of the population (N).</param>
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/// <param name="success">The number successes within the population (K, M).</param>
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/// <param name="draws">The number of draws without replacement (n).</param>
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public static void Samples(int[] values, int population, int success, int draws)
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{
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if (!(population >= 0 && success >= 0 && draws >= 0 && success <= population && draws <= population))
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{
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throw new ArgumentException("Invalid parametrization for the distribution.");
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}
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SamplesUnchecked(SystemRandomSource.Default, values, population, success, draws);
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}
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}
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}
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