// <copyright file="Bernoulli.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 System.Linq;
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using IStation.Numerics.Random;
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using IStation.Numerics.Threading;
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namespace IStation.Numerics.Distributions
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{
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/// <summary>
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/// Discrete Univariate Bernoulli distribution.
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/// The Bernoulli distribution is a distribution over bits. The parameter
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/// p specifies the probability that a 1 is generated.
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/// <a href="http://en.wikipedia.org/wiki/Bernoulli_distribution">Wikipedia - Bernoulli distribution</a>.
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/// </summary>
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public class Bernoulli : IDiscreteDistribution
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{
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System.Random _random;
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readonly double _p;
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/// <summary>
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/// Initializes a new instance of the Bernoulli class.
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/// </summary>
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/// <param name="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
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/// <exception cref="ArgumentOutOfRangeException">If the Bernoulli parameter is not in the range [0,1].</exception>
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public Bernoulli(double p)
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{
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if (!IsValidParameterSet(p))
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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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_p = p;
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}
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/// <summary>
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/// Initializes a new instance of the Bernoulli class.
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/// </summary>
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/// <param name="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
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/// <param name="randomSource">The random number generator which is used to draw random samples.</param>
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/// <exception cref="ArgumentOutOfRangeException">If the Bernoulli parameter is not in the range [0,1].</exception>
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public Bernoulli(double p, System.Random randomSource)
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{
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if (!IsValidParameterSet(p))
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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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_p = p;
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}
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/// <summary>
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/// A string representation of the distribution.
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/// </summary>
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/// <returns>a string representation of the distribution.</returns>
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public override string ToString()
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{
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return $"Bernoulli(p = {_p})";
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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="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
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public static bool IsValidParameterSet(double p)
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{
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return p >= 0.0 && p <= 1.0;
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}
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/// <summary>
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/// Gets the probability of generating a one. Range: 0 ≤ p ≤ 1.
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/// </summary>
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public double P => _p;
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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 mean of the distribution.
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/// </summary>
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public double Mean => _p;
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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(_p*(1.0 - _p));
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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 => _p*(1.0 - _p);
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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 => -(_p*Math.Log(_p)) - ((1.0 - _p)*Math.Log(1.0 - _p));
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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 => (1.0 - (2.0*_p))/Math.Sqrt(_p*(1.0 - _p));
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/// <summary>
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/// Gets the smallest element in the domain of the distributions which can be represented by an integer.
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/// </summary>
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public int Minimum => 0;
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/// <summary>
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/// Gets the largest element in the domain of the distributions which can be represented by an integer.
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/// </summary>
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public int Maximum => 1;
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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 => _p > 0.5 ? 1 : 0;
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/// <summary>
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/// Gets all modes of the distribution.
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/// </summary>
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public int[] Modes
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{
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get { return _p < 0.5 ? new[] { 0 } : P > 0.5 ? new[] { 1 } : new[] { 0, 1 }; }
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}
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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 => _p < 0.5 ? 0.0 : _p > 0.5 ? 1.0 : 0.5;
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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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if (k == 0)
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{
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return 1.0 - _p;
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}
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if (k == 1)
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{
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return _p;
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}
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return 0.0;
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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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if (k == 0)
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{
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return Math.Log(1.0 - _p);
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}
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return k == 1 ? Math.Log(_p) : double.NegativeInfinity;
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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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if (x < 0.0)
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{
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return 0.0;
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}
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if (x >= 1.0)
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{
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return 1.0;
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}
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return 1.0 - _p;
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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="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
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/// <returns>the probability mass at location <paramref name="k"/>.</returns>
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public static double PMF(double p, int k)
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{
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if (!(p >= 0.0 && p <= 1.0))
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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 (k == 0)
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{
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return 1.0 - p;
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}
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if (k == 1)
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{
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return p;
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}
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return 0.0;
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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="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
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/// <returns>the log probability mass at location <paramref name="k"/>.</returns>
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public static double PMFLn(double p, int k)
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{
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if (!(p >= 0.0 && p <= 1.0))
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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 (k == 0)
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{
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return Math.Log(1.0 - p);
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}
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return k == 1 ? Math.Log(p) : double.NegativeInfinity;
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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="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</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(double p, double x)
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{
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if (!(p >= 0.0 && p <= 1.0))
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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 < 0.0)
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{
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return 0.0;
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}
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if (x >= 1.0)
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{
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return 1.0;
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}
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return 1.0 - p;
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}
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/// <summary>
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/// Generates one sample from the Bernoulli distribution.
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/// </summary>
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/// <param name="rnd">The random source to use.</param>
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/// <param name="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
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/// <returns>A random sample from the Bernoulli distribution.</returns>
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static int SampleUnchecked(System.Random rnd, double p)
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{
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if (rnd.NextDouble() < p)
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{
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return 1;
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}
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return 0;
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}
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static void SamplesUnchecked(System.Random rnd, int[] values, double p)
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{
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var uniform = rnd.NextDoubles(values.Length);
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CommonParallel.For(0, values.Length, 4096, (a, b) =>
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{
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for (int i = a; i < b; i++)
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{
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values[i] = uniform[i] < p ? 1 : 0;
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}
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});
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}
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static IEnumerable<int> SamplesUnchecked(System.Random rnd, double p)
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{
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return rnd.NextDoubleSequence().Select(r => r < p ? 1 : 0);
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}
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/// <summary>
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/// Samples a Bernoulli distributed random variable.
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/// </summary>
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/// <returns>A sample from the Bernoulli distribution.</returns>
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public int Sample()
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{
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return SampleUnchecked(_random, _p);
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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, _p);
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}
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/// <summary>
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/// Samples an array of Bernoulli distributed random variables.
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/// </summary>
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/// <returns>a sequence of samples from the distribution.</returns>
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public IEnumerable<int> Samples()
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{
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while (true)
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{
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yield return SampleUnchecked(_random, _p);
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}
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}
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/// <summary>
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/// Samples a Bernoulli distributed 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="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
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/// <returns>A sample from the Bernoulli distribution.</returns>
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public static int Sample(System.Random rnd, double p)
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{
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if (!(p >= 0.0 && p <= 1.0))
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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, p);
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}
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/// <summary>
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/// Samples a sequence of Bernoulli distributed random variables.
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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="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
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/// <returns>a sequence of samples from the distribution.</returns>
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public static IEnumerable<int> Samples(System.Random rnd, double p)
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{
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if (!(p >= 0.0 && p <= 1.0))
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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, p);
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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="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
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/// <returns>a sequence of samples from the distribution.</returns>
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public static void Samples(System.Random rnd, int[] values, double p)
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{
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if (!(p >= 0.0 && p <= 1.0))
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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, p);
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}
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/// <summary>
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/// Samples a Bernoulli distributed random variable.
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/// </summary>
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/// <param name="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
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/// <returns>A sample from the Bernoulli distribution.</returns>
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public static int Sample(double p)
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{
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if (!(p >= 0.0 && p <= 1.0))
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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, p);
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}
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/// <summary>
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/// Samples a sequence of Bernoulli distributed random variables.
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/// </summary>
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/// <param name="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
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/// <returns>a sequence of samples from the distribution.</returns>
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public static IEnumerable<int> Samples(double p)
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{
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if (!(p >= 0.0 && p <= 1.0))
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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, p);
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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="p">The probability (p) of generating one. Range: 0 ≤ p ≤ 1.</param>
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/// <returns>a sequence of samples from the distribution.</returns>
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public static void Samples(int[] values, double p)
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{
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if (!(p >= 0.0 && p <= 1.0))
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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, p);
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}
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}
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}
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