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308 lines
11 KiB
308 lines
11 KiB
// <copyright file="ChiSquare.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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// http://mathnetnumerics.codeplex.com
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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 MathNet.Numerics.Properties;
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namespace MathNet.Numerics.Distributions
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{
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/// <summary>
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/// Continuous Univariate ChiSquare distribution.
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/// This distribution is a sum of the squares of k independent standard normal random variables.
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/// <a href="http://en.wikipedia.org/wiki/Chi-square_distribution">Wikipedia - ChiSquare distribution</a>.
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/// </summary>
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/// <remarks><para>The distribution will use the <see cref="System.Random"/> by default.
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/// Users can set the random number generator by using the <see cref="RandomSource"/> property.</para>
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/// <para>The statistics classes will check all the incoming parameters whether they are in the allowed
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/// range. This might involve heavy computation. Optionally, by setting Control.CheckDistributionParameters
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/// to <c>false</c>, all parameter checks can be turned off.</para></remarks>
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public class ChiSquare : IContinuousDistribution
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{
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System.Random _random;
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double _freedom;
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/// <summary>
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/// Initializes a new instance of the <see cref="ChiSquare"/> class.
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/// </summary>
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/// <param name="dof">The degrees of freedom for the ChiSquare distribution.</param>
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public ChiSquare(double dof)
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{
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_random = new System.Random();
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SetParameters(dof);
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}
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/// <summary>
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/// Initializes a new instance of the <see cref="ChiSquare"/> class.
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/// </summary>
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/// <param name="dof">The degrees of freedom for the ChiSquare distribution.</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 ChiSquare(double dof, System.Random randomSource)
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{
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_random = randomSource ?? new System.Random();
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SetParameters(dof);
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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 "ChiSquare(DoF = " + _freedom + ")";
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}
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/// <summary>
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/// Checks whether the parameters of the distribution are valid.
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/// </summary>
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/// <param name="dof">The degrees of freedom for the <c>ChiSquare</c> distribution.</param>
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/// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
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static bool IsValidParameterSet(double dof)
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{
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return dof > 0 && !Double.IsNaN(dof);
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}
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/// <summary>
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/// Sets the parameters of the distribution after checking their validity.
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/// </summary>
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/// <param name="dof">The degrees of freedom for the <c>ChiSquare</c> distribution.</param>
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/// <exception cref="ArgumentOutOfRangeException">When the parameters don't pass the <see cref="IsValidParameterSet"/> function.</exception>
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void SetParameters(double dof)
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{
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if (Control.CheckDistributionParameters && !IsValidParameterSet(dof))
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{
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throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
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}
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_freedom = dof;
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}
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/// <summary>
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/// Gets or sets the degrees of freedom of the <c>ChiSquare</c> distribution.
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/// </summary>
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public double DegreesOfFreedom
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{
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get { return _freedom; }
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set { SetParameters(value); }
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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 { return _random; }
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set { _random = value ?? new System.Random(); }
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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 { return _freedom; }
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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 { return 2.0*_freedom; }
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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
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{
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get { return Math.Sqrt(2.0 * _freedom); }
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}
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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
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{
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get { return (_freedom/2.0) + Math.Log(2.0*SpecialFunctions.Gamma(_freedom/2.0)) + ((1.0 - (_freedom/2.0))*SpecialFunctions.DiGamma(_freedom/2.0)); }
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}
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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 { return Math.Sqrt(8.0 / _freedom); }
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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 { return _freedom - 2.0; }
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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
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{
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get { return _freedom - (2.0 / 3.0); }
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}
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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
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{
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get { return 0.0; }
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}
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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
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{
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get { return double.PositiveInfinity; }
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}
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/// <summary>
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/// Computes the density of the distribution (PDF), i.e. dP(X <= x)/dx.
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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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public double Density(double x)
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{
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return (Math.Pow(x, (_freedom / 2.0) - 1.0) * Math.Exp(-x / 2.0)) / (Math.Pow(2.0, _freedom / 2.0) * SpecialFunctions.Gamma(_freedom / 2.0));
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}
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/// <summary>
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/// Computes the log density of the distribution (lnPDF), i.e. ln(dP(X <= x)/dx).
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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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public double DensityLn(double x)
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{
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return (-x / 2.0) + (((_freedom / 2.0) - 1.0) * Math.Log(x)) - ((_freedom / 2.0) * Math.Log(2)) - SpecialFunctions.GammaLn(_freedom / 2.0);
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}
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/// <summary>
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/// Computes the cumulative distribution (CDF) of the distribution, 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 SpecialFunctions.GammaLowerIncomplete(_freedom / 2.0, x / 2.0) / SpecialFunctions.Gamma(_freedom / 2.0);
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}
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/// <summary>
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/// Samples 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="dof">The degrees of freedom.</param>
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/// <returns>a random number from the distribution.</returns>
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internal static double SampleUnchecked(System.Random rnd, double dof)
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{
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//Use the simple method if the dof is an integer anyway
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if (Math.Floor(dof) == dof && dof < Int32.MaxValue)
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{
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double sum = 0;
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var n = (int) dof;
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for (var i = 0; i < n; i++)
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{
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sum += Math.Pow(Normal.Sample(rnd, 0.0, 1.0), 2);
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}
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return sum;
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}
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//Call the gamma function (see http://en.wikipedia.org/wiki/Gamma_distribution#Specializations
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//for a justification)
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return Gamma.SampleUnchecked(rnd, dof/2.0, .5);
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}
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/// <summary>
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/// Generates a sample from the <c>ChiSquare</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(RandomSource, _freedom);
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}
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/// <summary>
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/// Generates a sequence of samples from the <c>ChiSquare</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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while (true)
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{
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yield return SampleUnchecked(RandomSource, _freedom);
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}
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}
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/// <summary>
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/// Generates a sample from the <c>ChiSquare</c> 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="dof">The degrees of freedom.</param>
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/// <returns>a sample from the distribution. </returns>
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public static double Sample(System.Random rnd, double dof)
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{
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if (Control.CheckDistributionParameters && !IsValidParameterSet(dof))
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{
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throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
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}
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return SampleUnchecked(rnd, dof);
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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="dof">The degrees of freedom.</param>
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/// <returns>a sample from the distribution. </returns>
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public static IEnumerable<double> Samples(System.Random rnd, double dof)
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{
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if (Control.CheckDistributionParameters && !IsValidParameterSet(dof))
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{
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throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
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}
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while (true)
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{
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yield return SampleUnchecked(rnd, dof);
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}
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}
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}
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}
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