mathnet-numerics/src/Numerics/Distributions/ChiSquared.cs

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using System;
using System.Collections.Generic;
using MathNet.Numerics.Properties;
using MathNet.Numerics.Random;

namespace MathNet.Numerics.Distributions
{
    /// <summary>
    /// Continuous Univariate Chi-Squared distribution.
    /// This distribution is a sum of the squares of k independent standard normal random variables.
    /// <a href="http://en.wikipedia.org/wiki/Chi-square_distribution">Wikipedia - ChiSquare distribution</a>.
    /// </summary>
    public class ChiSquared : IContinuousDistribution
    {
        System.Random _random;

        double _freedom;

        /// <summary>
        /// Initializes a new instance of the <see cref="ChiSquared"/> class.
        /// </summary>
        /// <param name="freedom">The degrees of freedom (k) of the distribution. Range: k > 0.</param>
        public ChiSquared(double freedom)
        {
            _random = SystemRandomSource.Default;
            SetParameters(freedom);
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="ChiSquared"/> class.
        /// </summary>
        /// <param name="freedom">The degrees of freedom (k) of the distribution. Range: k > 0.</param>
        /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
        public ChiSquared(double freedom, System.Random randomSource)
        {
            _random = randomSource ?? SystemRandomSource.Default;
            SetParameters(freedom);
        }

        /// <summary>
        /// A string representation of the distribution.
        /// </summary>
        /// <returns>a string representation of the distribution.</returns>
        public override string ToString()
        {
            return "ChiSquared(k = " + _freedom + ")";
        }

        /// <summary>
        /// Sets the parameters of the distribution after checking their validity.
        /// </summary>
        /// <param name="freedom">The degrees of freedom (k) of the distribution. Range: k > 0.</param>
        /// <exception cref="ArgumentOutOfRangeException">When the parameters are out of range.</exception>
        void SetParameters(double freedom)
        {
            if (freedom <= 0.0 || Double.IsNaN(freedom))
            {
                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
            }

            _freedom = freedom;
        }

        /// <summary>
        /// Gets or sets the degrees of freedom (k) of the Chi-Squared distribution. Range: k > 0.
        /// </summary>
        public double DegreesOfFreedom
        {
            get { return _freedom; }
            set { SetParameters(value); }
        }

        /// <summary>
        /// Gets or sets the random number generator which is used to draw random samples.
        /// </summary>
        public System.Random RandomSource
        {
            get { return _random; }
            set { _random = value ?? SystemRandomSource.Default; }
        }

        /// <summary>
        /// Gets the mean of the distribution.
        /// </summary>
        public double Mean
        {
            get { return _freedom; }
        }

        /// <summary>
        /// Gets the variance of the distribution.
        /// </summary>
        public double Variance
        {
            get { return 2.0*_freedom; }
        }

        /// <summary>
        /// Gets the standard deviation of the distribution.
        /// </summary>
        public double StdDev
        {
            get { return Math.Sqrt(2.0 * _freedom); }
        }

        /// <summary>
        /// Gets the entropy of the distribution.
        /// </summary>
        public double Entropy
        {
            get { return (_freedom/2.0) + Math.Log(2.0*SpecialFunctions.Gamma(_freedom/2.0)) + ((1.0 - (_freedom/2.0))*SpecialFunctions.DiGamma(_freedom/2.0)); }
        }

        /// <summary>
        /// Gets the skewness of the distribution.
        /// </summary>
        public double Skewness
        {
            get { return Math.Sqrt(8.0 / _freedom); }
        }

        /// <summary>
        /// Gets the mode of the distribution.
        /// </summary>
        public double Mode
        {
            get { return _freedom - 2.0; }
        }

        /// <summary>
        /// Gets the median of the distribution.
        /// </summary>
        public double Median
        {
            get { return _freedom - (2.0 / 3.0); }
        }

        /// <summary>
        /// Gets the minimum of the distribution.
        /// </summary>
        public double Minimum
        {
            get { return 0.0; }
        }

        /// <summary>
        /// Gets the maximum of the distribution.
        /// </summary>
        public double Maximum
        {
            get { return double.PositiveInfinity; }
        }

        /// <summary>
        /// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
        /// </summary>
        /// <param name="x">The location at which to compute the density.</param>
        /// <returns>the density at <paramref name="x"/>.</returns>
        /// <seealso cref="PDF"/>
        public double Density(double x)
        {
            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));
        }

        /// <summary>
        /// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
        /// </summary>
        /// <param name="x">The location at which to compute the log density.</param>
        /// <returns>the log density at <paramref name="x"/>.</returns>
        /// <seealso cref="PDFLn"/>
        public double DensityLn(double x)
        {
            return (-x/2.0) + (((_freedom/2.0) - 1.0)*Math.Log(x)) - ((_freedom/2.0)*Math.Log(2)) - SpecialFunctions.GammaLn(_freedom/2.0);
        }

        /// <summary>
        /// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
        /// </summary>
        /// <param name="x">The location at which to compute the cumulative distribution function.</param>
        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
        /// <seealso cref="CDF"/>
        public double CumulativeDistribution(double x)
        {
            return SpecialFunctions.GammaLowerIncomplete(_freedom/2.0, x/2.0)/SpecialFunctions.Gamma(_freedom/2.0);
        }

        /// <summary>
        /// Generates a sample from the <c>ChiSquare</c> distribution.
        /// </summary>
        /// <returns>a sample from the distribution.</returns>
        public double Sample()
        {
            return SampleUnchecked(_random, _freedom);
        }

        /// <summary>
        /// Generates a sequence of samples from the <c>ChiSquare</c> distribution.
        /// </summary>
        /// <returns>a sequence of samples from the distribution.</returns>
        public IEnumerable<double> Samples()
        {
            while (true)
            {
                yield return SampleUnchecked(_random, _freedom);
            }
        }

        /// <summary>
        /// Samples the distribution.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="freedom">The degrees of freedom (k) of the distribution. Range: k > 0.</param>
        /// <returns>a random number from the distribution.</returns>
        static double SampleUnchecked(System.Random rnd, double freedom)
        {
            // Use the simple method if the degrees if freedom is an integer anyway
            if (Math.Floor(freedom) == freedom && freedom < Int32.MaxValue)
            {
                double sum = 0;
                var n = (int)freedom;
                for (var i = 0; i < n; i++)
                {
                    sum += Math.Pow(Normal.Sample(rnd, 0.0, 1.0), 2);
                }
                return sum;
            }

            //Call the gamma function (see http://en.wikipedia.org/wiki/Gamma_distribution#Specializations
            //for a justification)
            return Gamma.SampleUnchecked(rnd, freedom / 2.0, .5);
        }

        /// <summary>
        /// Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
        /// </summary>
        /// <param name="freedom">The degrees of freedom (k) of the distribution. Range: k > 0.</param>
        /// <param name="x">The location at which to compute the density.</param>
        /// <returns>the density at <paramref name="x"/>.</returns>
        /// <seealso cref="Density"/>
        public static double PDF(double freedom, double x)
        {
            if (freedom <= 0.0) throw new ArgumentOutOfRangeException("freedom", Resources.InvalidDistributionParameters);

            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));
        }

        /// <summary>
        /// Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
        /// </summary>
        /// <param name="freedom">The degrees of freedom (k) of the distribution. Range: k > 0.</param>
        /// <param name="x">The location at which to compute the density.</param>
        /// <returns>the log density at <paramref name="x"/>.</returns>
        /// <seealso cref="DensityLn"/>
        public static double PDFLn(double freedom, double x)
        {
            if (freedom <= 0.0) throw new ArgumentOutOfRangeException("freedom", Resources.InvalidDistributionParameters);

            return (-x/2.0) + (((freedom/2.0) - 1.0)*Math.Log(x)) - ((freedom/2.0)*Math.Log(2)) - SpecialFunctions.GammaLn(freedom/2.0);
        }

        /// <summary>
        /// Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
        /// </summary>
        /// <param name="x">The location at which to compute the cumulative distribution function.</param>
        /// <param name="freedom">The degrees of freedom (k) of the distribution. Range: k > 0.</param>
        /// <returns>the cumulative distribution at location <paramref name="x"/>.</returns>
        /// <seealso cref="CumulativeDistribution"/>
        public static double CDF(double freedom, double x)
        {
            if (freedom <= 0.0) throw new ArgumentOutOfRangeException("freedom", Resources.InvalidDistributionParameters);

            return SpecialFunctions.GammaLowerIncomplete(freedom/2.0, x/2.0)/SpecialFunctions.Gamma(freedom/2.0);
        }

        /// <summary>
        /// Generates a sample from the <c>ChiSquare</c> distribution.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="freedom">The degrees of freedom (k) of the distribution. Range: k > 0.</param>
        /// <returns>a sample from the distribution. </returns>
        public static double Sample(System.Random rnd, double freedom)
        {
            if (freedom <= 0.0) throw new ArgumentOutOfRangeException("freedom", Resources.InvalidDistributionParameters);

            return SampleUnchecked(rnd, freedom);
        }

        /// <summary>
        /// Generates a sequence of samples from the distribution.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="freedom">The degrees of freedom (k) of the distribution. Range: k > 0.</param>
        /// <returns>a sample from the distribution. </returns>
        public static IEnumerable<double> Samples(System.Random rnd, double freedom)
        {
            if (freedom <= 0.0) throw new ArgumentOutOfRangeException("freedom", Resources.InvalidDistributionParameters);

            while (true)
            {
                yield return SampleUnchecked(rnd, freedom);
            }
        }
    }
}