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

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

    /// <summary>
    /// Implements the Weibull distribution. For details about this distribution, see 
    /// <a href="http://en.wikipedia.org/wiki/Weibull_distribution">Wikipedia - Weibull distribution</a>.
    /// </summary>
    /// <remarks>
    /// <para>The Weibull distribution is parametrized by a shape and scale parameter.</para>
    /// <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 false, all parameter checks can be turned off.</para></remarks>
    public class Weibull : IContinuousDistribution
    {
        /// <summary>
        /// Weibull shape parameter.
        /// </summary>
        private double _shape;

        /// <summary>
        /// Weibull inverse scale parameter.
        /// </summary>
        private double _scale;

        /// <summary>
        /// Reusable intermediate result 1 / (<see cref="_scale"/> ^ <see cref="_shape"/>)
        /// </summary>
        /// <remarks>
        /// By caching this parameter we can get slightly better numerics precision
        /// in certain constellations without any additional computations.
        /// </remarks>
        private double _scalePowShapeInv;

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

        /// <summary>
        /// Initializes a new instance of the Weibull class.
        /// </summary>
        /// <param name="shape">The shape of the Weibull distribution.</param>
        /// <param name="scale">The inverse scale of the Weibull distribution.</param>
        public Weibull(double shape, double scale)
        {
            SetParameters(shape, scale);
            RandomSource = new Random();
        }

        /// <summary>
        /// A string representation of the distribution.
        /// </summary>
        /// <returns>a string representation of the distribution.</returns>
        public override string ToString()
        {
            return "Weibull(Shape = " + _shape + ", Scale = " + _scale + ")";
        }

        /// <summary>
        /// Checks whether the parameters of the distribution are valid. 
        /// </summary>
        /// <param name="shape">The shape of the Weibull distribution.</param>
        /// <param name="scale">The scale of the Weibull distribution.</param>
        /// <returns>True when the parameters positive valid floating point numbers, false otherwise.</returns>
        private static bool IsValidParameterSet(double shape, double scale)
        {
            if (shape <= 0.0 || scale <= 0.0 || Double.IsNaN(shape) || Double.IsNaN(scale))
            {
                return false;
            }

            return true;
        }

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

            _shape = shape;
            _scale = scale;
            _scalePowShapeInv = Math.Pow(scale, -shape);
        }

        /// <summary>
        /// Gets or sets the shape of the Weibull distribution.
        /// </summary>
        public double Shape
        {
            get
            {
                return _shape;
            }

            set
            {
                SetParameters(value, _scale);
            }
        }

        /// <summary>
        /// Gets or sets the scale of the Weibull distribution.
        /// </summary>
        public double Scale
        {
            get
            {
                return _scale;
            }

            set
            {
                SetParameters(_shape, 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 mean of the Weibull distribution.
        /// </summary>
        public double Mean
        {
            get
            {
                return _scale * SpecialFunctions.Gamma(1.0 + 1.0 / _shape);
            }
        }

        /// <summary>
        /// Gets the variance of the Weibull distribution.
        /// </summary>
        public double Variance
        {
            get
            {
                double mu = this.Mean;
                return _scale * _scale * SpecialFunctions.Gamma(1.0 + 2.0 / _shape) - mu * mu;
            }
        }

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

        /// <summary>
        /// Gets the entropy of the Weibull distribution.
        /// </summary>
        public double Entropy
        {
            get
            {
                throw new NotImplementedException();
            }
        }

        /// <summary>
        /// Gets the skewness of the Weibull distribution.
        /// </summary>
        public double Skewness
        {
            get
            {
                double mu = this.Mean;
                double sigma = this.StdDev;
                double sigma2 = sigma * sigma;
                double sigma3 = sigma2 * sigma;
                return (_scale * _scale * _scale * SpecialFunctions.Gamma(1.0 + 3.0 / _shape) 
                            - 3.0 * sigma2 * mu - mu * mu * mu) / sigma3;
            }
        }
        #endregion

        #region IContinuousDistribution implementation

        /// <summary>
        /// Gets the mode of the Weibull distribution.
        /// </summary>
        public double Mode
        {
            get
            {
                if (_shape <= 1.0)
                {
                    return 0.0;
                }

                return _scale * Math.Pow((_shape - 1.0) / _shape, 1.0 / _shape);
            }
        }

        /// <summary>
        /// Gets the median of the Weibull distribution.
        /// </summary>
        public double Median
        {
            get
            {
                return _scale * Math.Pow(Constants.Ln2, 1.0 / _shape);
            }
        }

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

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

        /// <summary>
        /// Computes the density of the Weibull 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)
            {
                if (x == 0.0 && _shape == 1.0)
                {
                    return _shape / _scale;
                }

                return _shape * Math.Pow(x / _scale, _shape - 1.0) * Math.Exp(-Math.Pow(x, _shape) * _scalePowShapeInv) / _scale;
            }

            return 0.0;
        }

        /// <summary>
        /// Computes the log density of the Weibull 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)
            {
                if (x == 0.0 && _shape == 1.0)
                {
                    return Math.Log(_shape) - Math.Log(_scale);
                }

                return Math.Log(_shape) + (_shape - 1.0) * Math.Log(x / _scale) - (Math.Pow(x, _shape) * _scalePowShapeInv) - Math.Log(_scale);
            }

            return double.NegativeInfinity;
        }

        /// <summary>
        /// Computes the cumulative distribution function of the Weibull 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 -SpecialFunctions.ExponentialMinusOne(-Math.Pow(x, _shape) * _scalePowShapeInv);
        }

        /// <summary>
        /// Generates a sample from the Weibull distribution.
        /// </summary>
        /// <returns>a sample from the distribution.</returns>
        public double Sample()
        {
            return SampleWeibull(RandomSource, _shape, _scale);
        }

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

        #endregion

        /// <summary>
        /// Generates a sample from the Weibull distribution.
        /// </summary>
        /// <param name="rng">The random number generator to use.</param>
        /// <param name="shape">The shape of the Weibull distribution from which to generate samples.</param>
        /// <param name="scale">The scale of the Weibull distribution from which to generate samples.</param>
        /// <returns>a sample from the distribution.</returns>
        public static double Sample(Random rng, double shape, double scale)
        {
            if (Control.CheckDistributionParameters && !IsValidParameterSet(shape, scale))
            {
                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
            }

            return SampleWeibull(rng, shape, scale);
        }

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

            while (true)
            {
                yield return SampleWeibull(rng, shape, scale);
            }
        }

        /// <summary>
        /// Generates one sample from the Weibull distribution. This method doesn't perform
        /// any parameter checks.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="shape">The shape of the Weibull distribution.</param>
        /// <param name="scale">The scale of the Weibull distribution.</param>
        /// <returns>A sample from a Weibull distributed random variable.</returns>
        internal static double SampleWeibull(System.Random rnd, double shape, double scale)
        {
            double x = rnd.NextDouble();
            return scale * Math.Pow(-Math.Log(x), 1.0 / shape);
        }
    }
}