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

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

namespace MathNet.Numerics.Distributions
{
    /// <summary>
    /// Discrete Univariate Bernoulli distribution.
    /// The Bernoulli distribution is a distribution over bits. The parameter
    /// p specifies the probability that a 1 is generated.
    /// <a href="http://en.wikipedia.org/wiki/Bernoulli_distribution">Wikipedia - Bernoulli 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 Bernoulli : IDiscreteDistribution
    {
        System.Random _random;

        double _p;

        /// <summary>
        /// Initializes a new instance of the Bernoulli class.
        /// </summary>
        /// <param name="p">The probability of generating one.</param>
        /// <exception cref="ArgumentOutOfRangeException">If the Bernoulli parameter is not in the range [0,1].</exception>
        public Bernoulli(double p)
        {
            _random = new System.Random();
            SetParameters(p);
        }

        /// <summary>
        /// Initializes a new instance of the Bernoulli class.
        /// </summary>
        /// <param name="p">The probability of generating one.</param>
        /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
        /// <exception cref="ArgumentOutOfRangeException">If the Bernoulli parameter is not in the range [0,1].</exception>
        public Bernoulli(double p, System.Random randomSource)
        {
            _random = randomSource ?? new System.Random();
            SetParameters(p);
        }

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

        /// <summary>
        /// Checks whether the parameters of the distribution are valid. 
        /// </summary>
        /// <param name="p">The probability of generating a one.</param>
        /// <returns><c>true</c> when the parameters are valid, <c>false</c> otherwise.</returns>
        static bool IsValidParameterSet(double p)
        {
            return p >= 0.0 && p <= 1.0;
        }

        /// <summary>
        /// Sets the parameters of the distribution after checking their validity.
        /// </summary>
        /// <param name="p">The probability of generating a one.</param>
        /// <exception cref="ArgumentOutOfRangeException">When the parameters are out of range.</exception>
        void SetParameters(double p)
        {
            if (Control.CheckDistributionParameters && !IsValidParameterSet(p))
            {
                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
            }

            _p = p;
        }

        /// <summary>
        /// Gets or sets the probability of generating a one.
        /// </summary>
        public double P
        {
            get { return _p; }
            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 _p; }
        }

        /// <summary>
        /// Gets the standard deviation of the distribution.
        /// </summary>
        public double StdDev
        {
            get { return Math.Sqrt(_p*(1.0 - _p)); }
        }

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

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

        /// <summary>
        /// Gets the skewness of the distribution.
        /// </summary>
        public double Skewness
        {
            get { return (1.0 - (2.0*_p))/Math.Sqrt(_p*(1.0 - _p)); }
        }

        /// <summary>
        /// Gets the smallest element in the domain of the distributions which can be represented by an integer.
        /// </summary>
        public int Minimum
        {
            get { return 0; }
        }

        /// <summary>
        /// Gets the largest element in the domain of the distributions which can be represented by an integer.
        /// </summary>
        public int Maximum
        {
            get { return 1; }
        }

        /// <summary>
        /// Gets the mode of the distribution.
        /// </summary>
        public int Mode
        {
            get { return _p > 0.5 ? 1 : 0; }
        }

        /// <summary>
        /// Gets the median of the distribution.
        /// </summary>
        public int Median
        {
            get { throw new NotSupportedException("The median of the Bernoulli distribution is undefined."); }
        }

        /// <summary>
        /// Computes the probability mass (PMF) at k, i.e. P(X = k).
        /// </summary>
        /// <param name="k">The location in the domain where we want to evaluate the probability mass function.</param>
        /// <returns>the probability mass at location <paramref name="k"/>.</returns>
        public double Probability(int k)
        {
            if (k == 0)
            {
                return 1.0 - _p;
            }

            if (k == 1)
            {
                return _p;
            }

            return 0.0;
        }

        /// <summary>
        /// Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
        /// </summary>
        /// <param name="k">The location in the domain where we want to evaluate the log probability mass function.</param>
        /// <returns>the log probability mass at location <paramref name="k"/>.</returns>
        public double ProbabilityLn(int k)
        {
            if (k == 0)
            {
                return Math.Log(1.0 - _p);
            }

            return k == 1 ? Math.Log(_p) : Double.NegativeInfinity;
        }

        /// <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>
        public double CumulativeDistribution(double x)
        {
            if (x < 0.0)
            {
                return 0.0;
            }

            if (x < 1.0)
            {
                return 1.0 - _p;
            }

            return 1.0;
        }

        /// <summary>
        /// Generates one sample from the Bernoulli distribution.
        /// </summary>
        /// <param name="rnd">The random source to use.</param>
        /// <param name="p">The probability of generating a one.</param>
        /// <returns>A random sample from the Bernoulli distribution.</returns>
        static int SampleUnchecked(System.Random rnd, double p)
        {
            if (rnd.NextDouble() < p)
            {
                return 1;
            }

            return 0;
        }

        /// <summary>
        /// Samples a Bernoulli distributed random variable.
        /// </summary>
        /// <returns>A sample from the Bernoulli distribution.</returns>
        public int Sample()
        {
            return SampleUnchecked(_random, _p);
        }

        /// <summary>
        /// Samples an array of Bernoulli distributed random variables.
        /// </summary>
        /// <returns>a sequence of samples from the distribution.</returns>
        public IEnumerable<int> Samples()
        {
            while (true)
            {
                yield return SampleUnchecked(_random, _p);
            }
        }

        /// <summary>
        /// Samples a Bernoulli distributed random variable.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="p">The probability of generating a 1.</param>
        /// <returns>A sample from the Bernoulli distribution.</returns>
        public static int Sample(System.Random rnd, double p)
        {
            if (Control.CheckDistributionParameters && !IsValidParameterSet(p))
            {
                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
            }

            return SampleUnchecked(rnd, p);
        }

        /// <summary>
        /// Samples a sequence of Bernoulli distributed random variables.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="p">The probability of generating a 1.</param>
        /// <returns>a sequence of samples from the distribution.</returns>
        public static IEnumerable<int> Samples(System.Random rnd, double p)
        {
            if (Control.CheckDistributionParameters && !IsValidParameterSet(p))
            {
                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
            }

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

    }
}