// <copyright file="FisherSnedecor.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) 2009-2013 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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using IStation.Numerics.RootFinding;
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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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/// Continuous Univariate F-distribution, also known as Fisher-Snedecor distribution.
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/// For details about this distribution, see
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/// <a href="http://en.wikipedia.org/wiki/F-distribution">Wikipedia - FisherSnedecor distribution</a>.
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/// </summary>
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public class FisherSnedecor : IContinuousDistribution
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{
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System.Random _random;
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readonly double _freedom1;
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readonly double _freedom2;
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/// <summary>
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/// Initializes a new instance of the <see cref="FisherSnedecor"/> class.
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/// </summary>
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/// <param name="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
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/// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
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public FisherSnedecor(double d1, double d2)
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{
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if (!IsValidParameterSet(d1, d2))
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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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_freedom1 = d1;
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_freedom2 = d2;
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}
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/// <summary>
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/// Initializes a new instance of the <see cref="FisherSnedecor"/> class.
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/// </summary>
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/// <param name="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
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/// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</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 FisherSnedecor(double d1, double d2, System.Random randomSource)
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{
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if (!IsValidParameterSet(d1, d2))
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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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_freedom1 = d1;
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_freedom2 = d2;
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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 $"FisherSnedecor(d1 = {_freedom1}, d2 = {_freedom2})";
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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="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
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/// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
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public static bool IsValidParameterSet(double d1, double d2)
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{
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return d1 > 0.0 && d2 > 0.0;
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}
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/// <summary>
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/// Gets the first degree of freedom (d1) of the distribution. Range: d1 > 0.
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/// </summary>
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public double DegreesOfFreedom1 => _freedom1;
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/// <summary>
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/// Gets the second degree of freedom (d2) of the distribution. Range: d2 > 0.
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/// </summary>
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public double DegreesOfFreedom2 => _freedom2;
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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
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{
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get
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{
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if (_freedom2 <= 2)
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{
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throw new NotSupportedException();
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}
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return _freedom2/(_freedom2 - 2.0);
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}
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}
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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
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{
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get
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{
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if (_freedom2 <= 4)
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{
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throw new NotSupportedException();
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}
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return (2.0*_freedom2*_freedom2*(_freedom1 + _freedom2 - 2.0))/(_freedom1*(_freedom2 - 2.0)*(_freedom2 - 2.0)*(_freedom2 - 4.0));
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}
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}
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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
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{
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get
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{
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if (_freedom2 <= 6)
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{
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throw new NotSupportedException();
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}
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return (((2.0*_freedom1) + _freedom2 - 2.0)*Math.Sqrt(8.0*(_freedom2 - 4.0)))/((_freedom2 - 6.0)*Math.Sqrt(_freedom1*(_freedom1 + _freedom2 - 2.0)));
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}
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}
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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 double Mode
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{
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get
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{
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if (_freedom1 <= 2)
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{
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throw new NotSupportedException();
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}
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return (_freedom2*(_freedom1 - 2.0))/(_freedom1*(_freedom2 + 2.0));
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}
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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 => 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 double Minimum => 0.0;
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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 double Maximum => double.PositiveInfinity;
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/// <summary>
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/// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
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/// </summary>
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/// <param name="x">The location at which to compute the density.</param>
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/// <returns>the density at <paramref name="x"/>.</returns>
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/// <seealso cref="PDF"/>
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public double Density(double x)
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{
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return Math.Sqrt(Math.Pow(_freedom1*x, _freedom1)*Math.Pow(_freedom2, _freedom2)/Math.Pow((_freedom1*x) + _freedom2, _freedom1 + _freedom2))/(x*SpecialFunctions.Beta(_freedom1/2.0, _freedom2/2.0));
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}
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/// <summary>
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/// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
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/// </summary>
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/// <param name="x">The location at which to compute the log density.</param>
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/// <returns>the log density at <paramref name="x"/>.</returns>
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/// <seealso cref="PDFLn"/>
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public double DensityLn(double x)
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{
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return Math.Log(Density(x));
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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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/// <seealso cref="CDF"/>
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public double CumulativeDistribution(double x)
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{
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return SpecialFunctions.BetaRegularized(_freedom1/2.0, _freedom2/2.0, _freedom1*x/((_freedom1*x) + _freedom2));
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}
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/// <summary>
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/// Computes the inverse of the cumulative distribution function (InvCDF) for the distribution
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/// at the given probability. This is also known as the quantile or percent point function.
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/// </summary>
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/// <param name="p">The location at which to compute the inverse cumulative density.</param>
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/// <returns>the inverse cumulative density at <paramref name="p"/>.</returns>
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/// <seealso cref="InvCDF"/>
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/// <remarks>WARNING: currently not an explicit implementation, hence slow and unreliable.</remarks>
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public double InverseCumulativeDistribution(double p)
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{
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return InvCDF(_freedom1, _freedom2, p);
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}
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/// <summary>
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/// Generates a sample from the <c>FisherSnedecor</c> distribution.
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/// </summary>
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/// <returns>a sample from the distribution.</returns>
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public double Sample()
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{
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return SampleUnchecked(_random, _freedom1, _freedom2);
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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(double[] values)
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{
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SamplesUnchecked(_random, values, _freedom1, _freedom2);
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}
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/// <summary>
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/// Generates a sequence of samples from the <c>FisherSnedecor</c> distribution.
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/// </summary>
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/// <returns>a sequence of samples from the distribution.</returns>
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public IEnumerable<double> Samples()
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{
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return SamplesUnchecked(_random, _freedom1, _freedom2);
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}
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/// <summary>
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/// Generates one sample from the <c>FisherSnedecor</c> distribution without 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="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
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/// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
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/// <returns>a <c>FisherSnedecor</c> distributed random number.</returns>
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static double SampleUnchecked(System.Random rnd, double d1, double d2)
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{
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return (ChiSquared.Sample(rnd, d1)*d2)/(ChiSquared.Sample(rnd, d2)*d1);
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}
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static void SamplesUnchecked(System.Random rnd, double[] values, double d1, double d2)
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{
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var values2 = new double[values.Length];
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ChiSquared.SamplesUnchecked(rnd, values, d1);
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ChiSquared.SamplesUnchecked(rnd, values2, d2);
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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] = (values[i]*d2)/(values2[i]*d1);
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}
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});
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}
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static IEnumerable<double> SamplesUnchecked(System.Random rnd, double d1, double d2)
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{
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while (true)
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{
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yield return SampleUnchecked(rnd, d1, d2);
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}
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}
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/// <summary>
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/// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
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/// </summary>
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/// <param name="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
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/// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
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/// <param name="x">The location at which to compute the density.</param>
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/// <returns>the density at <paramref name="x"/>.</returns>
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/// <seealso cref="Density"/>
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public static double PDF(double d1, double d2, double x)
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{
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if (d1 <= 0.0 || d2 <= 0.0)
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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 Math.Sqrt(Math.Pow(d1*x, d1)*Math.Pow(d2, d2)/Math.Pow((d1*x) + d2, d1 + d2))/(x*SpecialFunctions.Beta(d1/2.0, d2/2.0));
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}
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/// <summary>
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/// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
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/// </summary>
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/// <param name="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
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/// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
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/// <param name="x">The location at which to compute the density.</param>
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/// <returns>the log density at <paramref name="x"/>.</returns>
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/// <seealso cref="DensityLn"/>
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public static double PDFLn(double d1, double d2, double x)
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{
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return Math.Log(PDF(d1, d2, x));
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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="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
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/// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</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 d1, double d2, double x)
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{
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if (d1 <= 0.0 || d2 <= 0.0)
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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 SpecialFunctions.BetaRegularized(d1/2.0, d2/2.0, d1*x/(d1*x + d2));
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}
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/// <summary>
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/// Computes the inverse of the cumulative distribution function (InvCDF) for the distribution
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/// at the given probability. This is also known as the quantile or percent point function.
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/// </summary>
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/// <param name="p">The location at which to compute the inverse cumulative density.</param>
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/// <param name="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
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/// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
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/// <returns>the inverse cumulative density at <paramref name="p"/>.</returns>
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/// <seealso cref="InverseCumulativeDistribution"/>
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/// <remarks>WARNING: currently not an explicit implementation, hence slow and unreliable.</remarks>
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public static double InvCDF(double d1, double d2, double p)
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{
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if (d1 <= 0.0 || d2 <= 0.0)
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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 Brent.FindRoot(
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x => SpecialFunctions.BetaRegularized(d1/2.0, d2/2.0, d1*x/(d1*x + d2)) - p,
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0, 1000, accuracy: 1e-12);
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}
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/// <summary>
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/// Generates a sample 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="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
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/// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
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/// <returns>a sample from the distribution.</returns>
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public static double Sample(System.Random rnd, double d1, double d2)
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{
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if (d1 <= 0.0 || d2 <= 0.0)
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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, d1, d2);
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}
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/// <summary>
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/// Generates a sequence of samples 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="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
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/// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
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/// <returns>a sequence of samples from the distribution.</returns>
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public static IEnumerable<double> Samples(System.Random rnd, double d1, double d2)
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{
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if (d1 <= 0.0 || d2 <= 0.0)
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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, d1, d2);
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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="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
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/// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</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, double[] values, double d1, double d2)
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{
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if (d1 <= 0.0 || d2 <= 0.0)
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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, d1, d2);
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}
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/// <summary>
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/// Generates a sample from the distribution.
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/// </summary>
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/// <param name="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
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/// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
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/// <returns>a sample from the distribution.</returns>
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public static double Sample(double d1, double d2)
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{
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if (d1 <= 0.0 || d2 <= 0.0)
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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, d1, d2);
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}
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/// <summary>
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/// Generates a sequence of samples from the distribution.
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/// </summary>
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/// <param name="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
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/// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
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/// <returns>a sequence of samples from the distribution.</returns>
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public static IEnumerable<double> Samples(double d1, double d2)
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{
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if (d1 <= 0.0 || d2 <= 0.0)
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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, d1, d2);
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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="d1">The first degree of freedom (d1) of the distribution. Range: d1 > 0.</param>
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/// <param name="d2">The second degree of freedom (d2) of the distribution. Range: d2 > 0.</param>
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/// <returns>a sequence of samples from the distribution.</returns>
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public static void Samples(double[] values, double d1, double d2)
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{
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if (d1 <= 0.0 || d2 <= 0.0)
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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, d1, d2);
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}
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}
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}
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