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

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namespace MathNet.Numerics.Distributions
{
    using System;
    using System.Collections.Generic;
    using Properties;

    /// <summary>
    /// The exponential distribution is a distribution over the real numbers parameterized by one non-negative parameter.
    /// <a href="http://en.wikipedia.org/wiki/exponential_distribution">Wikipedia - exponential distribution</a>.
    /// </summary>
    /// <remarks>The distribution will use the <see cref="System.Random"/> by default. 
    /// <para>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 Exponential : IContinuousDistribution
    {
        /// <summary>
        /// The lambda parameter of the Exponential distribution. 
        /// </summary>
        double _lambda;

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

        /// <summary>
        /// Initializes a new instance of the <see cref="Exponential"/> class.
        /// </summary>
        /// <param name="lambda">The lambda parameter of the Exponential distribution.</param>
        public Exponential(double lambda)
        {
            _random = new Random();
            SetParameters(lambda);
        }

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

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

            _lambda = lambda;
        }

        /// <summary>
        /// Checks whether the parameters of the distribution are valid. 
        /// </summary>
        /// <param name="lambda">Lambda parameter.</param>
        /// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
        static bool IsValidParameterSet(double lambda)
        {
            return lambda >= 0.0;
        }

        /// <summary>
        /// Gets or sets the lambda parameter of the distribution.
        /// </summary>
        public double Lambda
        {
            get { return _lambda; }
            set { SetParameters(value); }
        }

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

        #region IDistribution Members

        /// <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 mean of the distribution.
        /// </summary>
        public double Mean
        {
            get { return 1.0/_lambda; }
        }

        /// <summary>
        /// Gets the variance of the distribution.
        /// </summary>
        public double Variance
        {
            get { return 1.0/(_lambda*_lambda); }
        }

        /// <summary>
        /// Gets the standard deviation of the distribution.
        /// </summary>
        public double StdDev
        {
            get { return 1.0/_lambda; }
        }

        /// <summary>
        /// Gets the entropy of the distribution.
        /// </summary>
        public double Entropy
        {
            get { return 1.0 - Math.Log(_lambda); }
        }

        /// <summary>
        /// Gets the skewness of the distribution.
        /// </summary>
        public double Skewness
        {
            get { return 2.0; }
        }

        /// <summary>
        /// Computes the cumulative distribution function of the 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 1.0 - Math.Exp(-_lambda*x);
            }

            return 0.0;
        }

        #endregion

        #region IContinuousDistribution Members

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

        /// <summary>
        /// Gets the median of the distribution.
        /// </summary>
        public double Median
        {
            get { return Math.Log(2.0)/_lambda; }
        }

        /// <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.
        /// </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 _lambda*Math.Exp(-_lambda*x);
            }

            return 0.0;
        }

        /// <summary>
        /// Computes the log density of the 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)
        {
            return Math.Log(_lambda) - (_lambda*x);
        }

        #endregion

        /// <summary>
        /// Samples the distribution.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="lambda">The lambda parameter of the Exponential distribution.</param>
        /// <returns>a random number from the distribution.</returns>
        internal static double SampleUnchecked(Random rnd, double lambda)
        {
            var r = rnd.NextDouble();
            while (r == 0.0)
            {
                r = rnd.NextDouble();
            }

            return -Math.Log(r)/lambda;
        }

        /// <summary>
        /// Draws a random sample from the distribution.
        /// </summary>
        /// <returns>A random number from this distribution.</returns>
        public double Sample()
        {
            return SampleUnchecked(RandomSource, _lambda);
        }

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

        /// <summary>
        /// Draws a random sample from the distribution.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="lambda">The lambda parameter of the Exponential distribution.</param>
        /// <returns>A random number from this distribution.</returns>
        public static double Sample(Random rnd, double lambda)
        {
            if (Control.CheckDistributionParameters && !IsValidParameterSet(lambda))
            {
                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
            }

            return SampleUnchecked(rnd, lambda);
        }

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

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