mathnet-numerics/src/Numerics/Distributions/Continuous/LogNormal.cs

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

namespace MathNet.Numerics.Distributions
{
    using System;

    /// <summary>
    /// Implements the univariate Log-Normal distribution. For details about this distribution, see 
    /// <a href="http://en.wikipedia.org/wiki/Log-normal_distribution">Wikipedia - Log-Normal distribution</a>.
    /// </summary>
    /// <remarks><para>The distribution will use the <see cref="System.Random"/> by default. 
    /// Users can get/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 LogNormal : IContinuousDistribution
    {
        /// <summary>
        /// Keeps track of the mu of the logarithm of the log-log-normal distribution.
        /// </summary>
        double _mu;

        /// <summary>
        /// Keeps track of the standard deviation of the logarithm of the log-log-normal distribution.
        /// </summary>
        double _sigma;

        /// <summary>
        /// The distribution's random number generator.
        /// </summary>
        Random _random;

        /// <summary>
        /// Initializes a new instance of the <see cref="LogNormal"/> class. 
        /// The distribution will be initialized with the default <seealso cref="System.Random"/>
        /// random number generator.
        /// </summary>
        /// <param name="mu">The mu of the logarithm of the distribution.</param>
        /// <param name="sigma">The standard deviation of the logarithm of the distribution.</param>
        public LogNormal(double mu, double sigma)
        {
            _random = new Random();
            SetParameters(mu, sigma);
        }

        /// <summary>
        /// Initializes a new instance of the <see cref="LogNormal"/> class. 
        /// The distribution will be initialized with the default <seealso cref="System.Random"/>
        /// random number generator.
        /// </summary>
        /// <param name="mu">The mu of the logarithm of the distribution.</param>
        /// <param name="sigma">The standard deviation of the logarithm of the distribution.</param>
        /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
        public LogNormal(double mu, double sigma, Random randomSource)
        {
            _random = randomSource ?? new Random();
            SetParameters(mu, sigma);
        }

        /// <summary>
        /// Constructs a log-normal distribution with the desired mean and variance. The distribution will
        /// be initialized with the default <seealso cref="System.Random"/> random number generator.
        /// </summary>
        /// <param name="mean">The mean of the log-normal distribution.</param>
        /// <param name="var">The variance of the log-normal distribution.</param>
        /// <returns>a log-normal distribution.</returns>
        public static LogNormal WithMeanVariance(double mean, double var)
        {
            var sigma2 = Math.Log(var / (mean * mean) + 1.0);
            return new LogNormal(Math.Log(mean) - sigma2 / 2.0, Math.Sqrt(sigma2));
        }

        /// <summary>
        /// Estimates the log-normal distribution parameters from sample data with maximum-likelihood.
        /// </summary>
        public static LogNormal Estimate(IEnumerable<double> samples)
        {
            var muSigma2 = samples.Select(s => Math.Log(s)).MeanVariance();
            return new LogNormal(muSigma2.Item1, Math.Sqrt(muSigma2.Item2));
        }

        /// <summary>
        /// A string representation of the distribution.
        /// </summary>
        /// <returns>a string representation of the distribution.</returns>
        public override string ToString()
        {
            return "LogNormal(Mu = " + _mu + ", Sigma = " + _sigma + ")";
        }

        /// <summary>
        /// Checks whether the parameters of the distribution are valid. 
        /// </summary>
        /// <param name="mu">The mu of the logarithm of the distribution.</param>
        /// <param name="sigma">The standard deviation of the logarithm of the distribution.</param>
        /// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
        static bool IsValidParameterSet(double mu, double sigma)
        {
            if (sigma < 0.0 || Double.IsNaN(mu) || Double.IsNaN(mu) || Double.IsNaN(sigma))
            {
                return false;
            }

            return true;
        }

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

            _mu = mu;
            _sigma = sigma;
        }

        /// <summary>
        /// Gets or sets the mean of the logarithm of the log-normal.
        /// </summary>
        public double Mu
        {
            get { return _mu; }
            set { SetParameters(value, _sigma); }
        }

        /// <summary>
        /// Gets or sets the standard deviation of the logarithm of the log-normal.
        /// </summary>
        public double Sigma
        {
            get { return _sigma; }
            set { SetParameters(_mu, value); }
        }

        #region IDistribution implementation

        /// <summary>
        /// Gets or sets the random number generator which is used to draw random samples.
        /// </summary>
        public Random RandomSource
        {
            get { return _random; }
            set
            {
                if (value == null)
                {
                    throw new ArgumentNullException();
                }

                _random = value;
            }
        }

        /// <summary>
        /// Gets the mu of the log-normal distribution.
        /// </summary>
        public double Mean
        {
            get { return Math.Exp(_mu + (_sigma*_sigma/2.0)); }
        }

        /// <summary>
        /// Gets the variance of the log-normal distribution.
        /// </summary>
        public double Variance
        {
            get
            {
                var sigma2 = _sigma*_sigma;
                return (Math.Exp(sigma2) - 1.0)*Math.Exp(_mu + _mu + sigma2);
            }
        }

        /// <summary>
        /// Gets the standard deviation of the log-normal distribution.
        /// </summary>
        public double StdDev
        {
            get
            {
                var sigma2 = _sigma*_sigma;
                return Math.Sqrt((Math.Exp(sigma2) - 1.0)*Math.Exp(_mu + _mu + sigma2));
            }
        }

        /// <summary>
        /// Gets the entropy of the log-normal distribution.
        /// </summary>
        public double Entropy
        {
            get { return 0.5 + Math.Log(_sigma) + _mu + Constants.LogSqrt2Pi; }
        }

        /// <summary>
        /// Gets the skewness of the log-normal distribution.
        /// </summary>
        public double Skewness
        {
            get
            {
                var expsigma2 = Math.Exp(_sigma*_sigma);
                return (expsigma2 + 2.0)*Math.Sqrt(expsigma2 - 1);
            }
        }

        #endregion

        #region IContinuousDistribution implementation

        /// <summary>
        /// Gets the mode of the log-normal distribution.
        /// </summary>
        public double Mode
        {
            get { return Math.Exp(_mu - (_sigma*_sigma)); }
        }

        /// <summary>
        /// Gets the median of the log-normal distribution.
        /// </summary>
        public double Median
        {
            get { return Math.Exp(_mu); }
        }

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

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

        /// <summary>
        /// Computes the density of the log-normal distribution.
        /// </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)
        {
            if (x < 0.0)
            {
                return 0.0;
            }

            var a = (Math.Log(x) - _mu)/_sigma;
            return Math.Exp(-0.5*a*a)/(x*_sigma*Constants.Sqrt2Pi);
        }

        /// <summary>
        /// Computes the log density of the log-normal distribution.
        /// </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)
        {
            if (x < 0.0)
            {
                return Double.NegativeInfinity;
            }

            var a = (Math.Log(x) - _mu)/_sigma;
            return (-0.5*a*a) - Math.Log(x*_sigma) - Constants.LogSqrt2Pi;
        }

        /// <summary>
        /// Computes the cumulative distribution function of the log-normal distribution.
        /// </summary>
        /// <param name="x">The location at which to compute the cumulative density.</param>
        /// <returns>the cumulative density at <paramref name="x"/>.</returns>
        public double CumulativeDistribution(double x)
        {
            if (x < 0.0)
            {
                return 0.0;
            }

            return 0.5*(1.0 + SpecialFunctions.Erf((Math.Log(x) - _mu)/(_sigma*Constants.Sqrt2)));
        }

        #endregion

        /// <summary>
        /// Generates a sample from the log-normal distribution using the <i>Box-Muller</i> algorithm.
        /// </summary>
        /// <returns>a sample from the distribution.</returns>
        public double Sample()
        {
            return Math.Exp(Normal.SampleUnchecked(RandomSource, _mu, _sigma));
        }

        /// <summary>
        /// Generates a sequence of samples from the log-normal distribution using the <i>Box-Muller</i> algorithm.
        /// </summary>
        /// <returns>a sequence of samples from the distribution.</returns>
        public IEnumerable<double> Samples()
        {
            while (true)
            {
                var sample = Normal.SampleUncheckedBoxMuller(RandomSource);
                yield return Math.Exp(_mu + (_sigma*sample.Item1));
                yield return Math.Exp(_mu + (_sigma*sample.Item2));
            }
        }

        /// <summary>
        /// Generates a sample from the log-normal distribution using the <i>Box-Muller</i> algorithm.
        /// </summary>
        /// <param name="rng">The random number generator to use.</param>
        /// <param name="mu">The mu of the logarithm of the distribution.</param>
        /// <param name="sigma">The standard deviation of the logarithm of the distribution.</param>
        /// <returns>a sample from the distribution.</returns>
        public static double Sample(Random rng, double mu, double sigma)
        {
            if (Control.CheckDistributionParameters && !IsValidParameterSet(mu, sigma))
            {
                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
            }

            return Math.Exp(Normal.SampleUnchecked(rng, mu, sigma));
        }

        /// <summary>
        /// Generates a sequence of samples from the log-normal distribution using the <i>Box-Muller</i> algorithm.
        /// </summary>
        /// <param name="rng">The random number generator to use.</param>
        /// <param name="mu">The mu of the logarithm of the distribution.</param>
        /// <param name="sigma">The standard deviation of the logarithm of the distribution.</param>
        /// <returns>a sequence of samples from the distribution.</returns>
        public static IEnumerable<double> Samples(Random rng, double mu, double sigma)
        {
            if (Control.CheckDistributionParameters && !IsValidParameterSet(mu, sigma))
            {
                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
            }

            while (true)
            {
                var sample = Normal.SampleUncheckedBoxMuller(rng);
                yield return Math.Exp(mu + (sigma*sample.Item1));
                yield return Math.Exp(mu + (sigma*sample.Item2));
            }
        }
    }
}