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

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

namespace MathNet.Numerics.Distributions
{
    /// <summary>
    /// Continuous Univariate Chi distribution.
    /// This distribution is a continuous probability distribution. The distribution usually arises when a k-dimensional vector's orthogonal 
    /// components are independent and each follow a standard normal distribution. The length of the vector will 
    /// then have a chi distribution.
    /// <a href="http://en.wikipedia.org/wiki/Chi_distribution">Wikipedia - Chi distribution</a>.
    /// </summary>
    /// <remarks><para>The distribution will use the <see cref="System.Random"/> by default. 
    /// Users can set the random number generator by using the <see cref="RandomSource"/> property.</para>
    /// <para>The statistics classes will check all the incoming parameters whether they are in the allowed
    /// range. This might involve heavy computation. Optionally, by setting Control.CheckDistributionParameters
    /// to <c>false</c>, all parameter checks can be turned off.</para></remarks>
    public class Chi : IContinuousDistribution
    {
        System.Random _random;

        double _freedom;

        /// <summary>
        /// Initializes a new instance of the <see cref="Chi"/> class. 
        /// </summary>
        /// <param name="dof">The degrees of freedom for the Chi distribution.</param>
        public Chi(double dof)
        {
            _random = new System.Random();
            SetParameters(dof);
        }

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

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

        /// <summary>
        /// Checks whether the parameters of the distribution are valid.
        /// </summary>
        /// <param name="dof">The degrees of freedom for the Chi distribution.</param>
        /// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
        static bool IsValidParameterSet(double dof)
        {
            return dof > 0.0;
        }

        /// <summary>
        /// Sets the parameters of the distribution after checking their validity.
        /// </summary>
        /// <param name="dof">The degrees of freedom for the Chi distribution.</param>
        /// <exception cref="ArgumentOutOfRangeException">When the parameters don't pass the <see cref="IsValidParameterSet"/> function.</exception>
        void SetParameters(double dof)
        {
            if (Control.CheckDistributionParameters && !IsValidParameterSet(dof))
            {
                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
            }

            _freedom = dof;
        }

        /// <summary>
        /// Gets or sets the degrees of freedom of the Chi distribution.
        /// </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 ?? new System.Random(); }
        }

        /// <summary>
        /// Gets the mean of the distribution.
        /// </summary>
        public double Mean
        {
            get { return Constants.Sqrt2*(SpecialFunctions.Gamma((_freedom + 1.0)/2.0)/SpecialFunctions.Gamma(_freedom/2.0)); }
        }

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

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

        /// <summary>
        /// Gets the entropy of the distribution.
        /// </summary>
        public double Entropy
        {
            get { return SpecialFunctions.GammaLn(_freedom/2.0) + ((_freedom - Math.Log(2) - ((_freedom - 1.0)*SpecialFunctions.DiGamma(_freedom/2.0)))/2.0); }
        }

        /// <summary>
        /// Gets the skewness of the distribution.
        /// </summary>
        public double Skewness
        {
            get
            {
                var sigma = StdDev;
                return (Mean*(1.0 - (2.0*(sigma*sigma))))/(sigma*sigma*sigma);
            }
        }

        /// <summary>
        /// Gets the mode of the distribution.
        /// </summary>
        public double Mode
        {
            get
            {
                if (_freedom < 1)
                {
                    throw new NotSupportedException();
                }

                return Math.Sqrt(_freedom - 1.0);
            }
        }

        /// <summary>
        /// Gets the median of the distribution.
        /// </summary>
        public double Median
        {
            get { throw new NotSupportedException(); }
        }

        /// <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 density of the distribution (PDF), i.e. dP(X &lt;= x)/dx.
        /// </summary>
        /// <param name="x">The location at which to compute the density.</param>
        /// <returns>the density at <paramref name="x"/>.</returns>
        public double Density(double x)
        {
            return (Math.Pow(2.0, 1.0 - (_freedom/2.0))*Math.Pow(x, _freedom - 1.0)*Math.Exp(-x*x/2.0))/SpecialFunctions.Gamma(_freedom/2.0);
        }

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

        /// <summary>
        /// Computes the cumulative distribution (CDF) of the distribution, i.e. P(X &lt;= 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>
        public double CumulativeDistribution(double x)
        {
            return SpecialFunctions.GammaLowerIncomplete(_freedom/2.0, x*x/2.0)/SpecialFunctions.Gamma(_freedom/2.0);
        }

        /// <summary>
        /// Samples the distribution.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="dof">Degrees of Freedom</param>
        /// <returns>a random number from the distribution.</returns>
        internal static double SampleUnchecked(System.Random rnd, int dof)
        {
            double sum = 0;
            for (var i = 0; i < dof; i++)
            {
                sum += Math.Pow(Normal.Sample(rnd, 0.0, 1.0), 2);
            }

            return Math.Sqrt(sum);
        }

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

        /// <summary>
        /// Generates a sequence of samples from the Chi distribution.
        /// </summary>
        /// <returns>a sequence of samples from the distribution.</returns>
        public IEnumerable<double> Samples()
        {
            var dof = (int) _freedom;
            while (true)
            {
                yield return SampleUnchecked(RandomSource, dof);
            }
        }

        /// <summary>
        /// Generates a sample from the distribution.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="dof">Degrees of Freedom</param>
        /// <returns>a sample from the distribution.</returns>
        public static double Sample(System.Random rnd, int dof)
        {
            if (Control.CheckDistributionParameters && !IsValidParameterSet(dof))
            {
                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
            }

            return SampleUnchecked(rnd, dof);
        }

        /// <summary>
        /// Generates a sequence of samples from the distribution.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="dof">Degrees of Freedom</param>
        /// <returns>a sequence of samples from the distribution.</returns>
        public static IEnumerable<double> Samples(System.Random rnd, int dof)
        {
            if (Control.CheckDistributionParameters && !IsValidParameterSet(dof))
            {
                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
            }

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