mathnet-numerics/src/Numerics/Distributions/Discrete/Binomial.cs

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

    /// <summary>
    /// Implements the binomial distribution. For details about this distribution, see 
    /// <a href="http://en.wikipedia.org/wiki/Binomial_distribution">Wikipedia - Binomial distribution</a>.
    /// </summary>
    /// <remarks><para>The distribution is parameterized by a probability (between 0.0 and 1.0).</para>
    /// <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 Binomial : IDiscreteDistribution
    {
        /// <summary>
        /// Stores the normalized binomial probability.
        /// </summary>
        double _p;

        /// <summary>
        /// The number of trials.
        /// </summary>
        int _n;

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

        /// <summary>
        /// Initializes a new instance of the Binomial class.
        /// </summary>
        /// <param name="p">The success probability of a trial.</param>
        /// <param name="n">The number of trials.</param>
        /// <exception cref="ArgumentOutOfRangeException">If <paramref name="p"/> is not in the interval [0.0,1.0].</exception>
        /// <exception cref="ArgumentOutOfRangeException">If <paramref name="n"/> is negative.</exception>
        public Binomial(double p, int n)
        {
            _random = new Random();
            SetParameters(p, n);
        }

        /// <summary>
        /// Initializes a new instance of the Binomial class.
        /// </summary>
        /// <param name="p">The success probability of a trial.</param>
        /// <param name="n">The number of trials.</param>
        /// <param name="randomSource">The random number generator which is used to draw random samples.</param>
        /// <exception cref="ArgumentOutOfRangeException">If <paramref name="p"/> is not in the interval [0.0,1.0].</exception>
        /// <exception cref="ArgumentOutOfRangeException">If <paramref name="n"/> is negative.</exception>
        public Binomial(double p, int n, Random randomSource)
        {
            _random = randomSource ?? new Random();
            SetParameters(p, n);
        }

        /// <summary>
        /// A string representation of the distribution.
        /// </summary>
        /// <returns>a string representation of the distribution.</returns>
        public override string ToString()
        {
            return "Binomial(Success Probability = " + _p + ", Number of Trials = " + _n + ")";
        }

        /// <summary>
        /// Checks whether the parameters of the distribution are valid. 
        /// </summary>
        /// <param name="p">The success probability of a trial.</param>
        /// <param name="n">The number of trials.</param>
        /// <returns><c>false</c> <paramref name="p"/> is not in the interval [0.0,1.0] or <paramref name="n"/> is negative, <c>true</c> otherwise.</returns>
        static bool IsValidParameterSet(double p, int n)
        {
            if (p < 0.0 || p > 1.0 || Double.IsNaN(p))
            {
                return false;
            }

            if (n < 0)
            {
                return false;
            }

            return true;
        }

        /// <summary>
        /// Sets the parameters of the distribution after checking their validity.
        /// </summary>
        /// <param name="p">The success probability of a trial.</param>
        /// <param name="n">The number of trials.</param>
        /// <exception cref="ArgumentOutOfRangeException">If <paramref name="p"/> is not in the interval [0.0,1.0].</exception>
        /// <exception cref="ArgumentOutOfRangeException">If <paramref name="n"/> is negative.</exception>
        void SetParameters(double p, int n)
        {
            if (Control.CheckDistributionParameters && !IsValidParameterSet(p, n))
            {
                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
            }

            _p = p;
            _n = n;
        }

        /// <summary>
        /// Gets or sets the success probability.
        /// </summary>
        public double P
        {
            get { return _p; }
            set { SetParameters(value, _n); }
        }

        /// <summary>
        /// Gets or sets the number of trials.
        /// </summary>
        public int N
        {
            get { return _n; }
            set { SetParameters(_p, value); }
        }

        #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 _p*_n; }
        }

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

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

        /// <summary>
        /// Gets the entropy of the distribution.
        /// </summary>
        public double Entropy
        {
            get
            {
                if (_p == 0.0 || _p == 1.0)
                {
                    return 0.0;
                }

                var e = 0.0;
                for (var i = 0; i <= _n; i++)
                {
                    var p = Probability(i);
                    e -= p*Math.Log(p);
                }

                return e;
            }
        }

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

        /// <summary>
        /// Computes the cumulative distribution function of the Binomial 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;
            }

            if (x > _n)
            {
                return 1.0;
            }

            var cdf = 0.0;
            for (var i = 0; i <= (int) Math.Floor(x); i++)
            {
                cdf += Combinatorics.Combinations(_n, i)*Math.Pow(_p, i)*Math.Pow(1.0 - _p, _n - i);
            }

            return cdf;
        }

        #endregion

        #region IDiscreteDistribution Members

        /// <summary>
        /// Gets the mode of the distribution.
        /// </summary>
        public int Mode
        {
            get
            {
                if (_p == 1.0)
                {
                    return _n;
                }

                if (_p == 0.0)
                {
                    return 0;
                }

                return (int) Math.Floor((_n + 1)*_p);
            }
        }

        /// <summary>
        /// Gets the median of the distribution.
        /// </summary>
        public int Median
        {
            get { return (int) Math.Floor(_p*_n); }
        }

        /// <summary>
        /// Computes values of the probability mass function.
        /// </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 0.0;
            }

            if (k > _n)
            {
                return 0.0;
            }

            if (_p == 0.0 && k == 0)
            {
                return 1.0;
            }

            if (_p == 0.0)
            {
                return 0.0;
            }

            if (_p == 1.0 && k == _n)
            {
                return 1.0;
            }

            if (_p == 1.0)
            {
                return 0.0;
            }

            return SpecialFunctions.Binomial(_n, k)*Math.Pow(_p, k)*Math.Pow(1.0 - _p, _n - k);
        }

        /// <summary>
        /// Computes values of the log probability mass function.
        /// </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 Double.NegativeInfinity;
            }

            if (k > _n)
            {
                return Double.NegativeInfinity;
            }

            if (_p == 0.0 && k == 0)
            {
                return 0.0;
            }

            if (_p == 0.0)
            {
                return Double.NegativeInfinity;
            }

            if (_p == 1.0 && k == _n)
            {
                return 0.0;
            }

            if (_p == 1.0)
            {
                return Double.NegativeInfinity;
            }

            return SpecialFunctions.BinomialLn(_n, k) + (k*Math.Log(_p)) + ((_n - k)*Math.Log(1.0 - _p));
        }

        #endregion

        /// <summary>
        /// Generates a sample from the Binomial distribution without doing parameter checking.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="p">The success probability of a trial; must be in the interval [0.0, 1.0].</param>
        /// <param name="n">The number of trials; must be positive.</param>
        /// <returns>The number of successful trials.</returns>
        internal static int SampleUnchecked(Random rnd, double p, int n)
        {
            var k = 0;
            for (var i = 0; i < n; i++)
            {
                k += rnd.NextDouble() < p ? 1 : 0;
            }

            return k;
        }

        /// <summary>
        /// Samples a Binomially distributed random variable.
        /// </summary>
        /// <returns>The number of successes in N trials.</returns>
        public int Sample()
        {
            return SampleUnchecked(RandomSource, _p, _n);
        }

        /// <summary>
        /// Samples an array of Binomially distributed random variables.
        /// </summary>
        /// <returns>a sequence of successes in N trials.</returns>
        public IEnumerable<int> Samples()
        {
            while (true)
            {
                yield return SampleUnchecked(RandomSource, _p, _n);
            }
        }

        /// <summary>
        /// Samples a binomially distributed random variable.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="p">The success probability of a trial; must be in the interval [0.0, 1.0].</param>
        /// <param name="n">The number of trials; must be positive.</param>
        /// <returns>The number of successes in <paramref name="n"/> trials.</returns>
        public static int Sample(Random rnd, double p, int n)
        {
            if (Control.CheckDistributionParameters && !IsValidParameterSet(p, n))
            {
                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
            }

            return SampleUnchecked(rnd, p, n);
        }

        /// <summary>
        /// Samples a sequence of binomially distributed random variable.
        /// </summary>
        /// <param name="rnd">The random number generator to use.</param>
        /// <param name="p">The success probability of a trial; must be in the interval [0.0, 1.0].</param>
        /// <param name="n">The number of trials; must be positive.</param>
        /// <returns>a sequence of successes in <paramref name="n"/> trials.</returns>
        public static IEnumerable<int> Samples(Random rnd, double p, int n)
        {
            if (Control.CheckDistributionParameters && !IsValidParameterSet(p, n))
            {
                throw new ArgumentOutOfRangeException(Resources.InvalidDistributionParameters);
            }

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