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richard-churchman
cc0a2bee21
Included open-source Accord.net library code natively to the solution given the deprecated state of that project. Accord.net will be supported inside Jube for own needs (such as upgrading to .Net 7+). Accord.net libraries modified to compile to .Net 6. Modified Accord.net libraries to better support Newtonsoft Json.net serialisation. Included annotations in the Accord.net libraries to house important dependency statistics. Serialised json can be used independently of Jube to recall a Neural Network. Removal of Binary Serializer totally as a precursor to the projects support of .Net 7+. Extensive bug fixing in crucial functions of Neural Network training and recall. While this part of the system remains in Alpha, it is substantially more fit for purpose.
292 lines
11 KiB
C#
292 lines
11 KiB
C#
// Accord Statistics Library
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// The Accord.NET Framework
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// http://accord-framework.net
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//
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// Copyright © César Souza, 2009-2017
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// cesarsouza at gmail.com
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//
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// This library is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 2.1 of the License, or (at your option) any later version.
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//
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// This library is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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// Lesser General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License along with this library; if not, write to the Free Software
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// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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//
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namespace Accord.Statistics.Distributions.Univariate
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{
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using System;
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using Accord.Math;
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using Accord.Compat;
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/// <summary>
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/// Negative Binomial distribution.
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/// </summary>
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///
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/// <remarks>
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/// <para>
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/// The negative binomial distribution is a discrete probability distribution of the number
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/// of successes in a sequence of Bernoulli trials before a specified (non-random) number of
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/// failures (denoted r) occur. For example, if one throws a die repeatedly until the third
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/// time “1” appears, then the probability distribution of the number of non-“1”s that had
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/// appeared will be negative binomial.</para>
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///
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/// <para>
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/// References:
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/// <list type="bullet">
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/// <item><description><a href="http://en.wikipedia.org/wiki/Negative_binomial_distribution">
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/// Wikipedia, The Free Encyclopedia. Negative Binomial distribution.
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/// Available from: http://en.wikipedia.org/wiki/Negative_binomial_distribution </a></description></item>
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/// </list></para>
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/// </remarks>
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///
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/// <example>
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/// <code>
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/// // Create a new Negative Binomial distribution with r = 7 and p = 0.42
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/// var dist = new NegativeBinomialDistribution(failures: 7, probability: 0.42);
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///
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/// // Common measures
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/// double mean = dist.Mean; // 5.068965517241379
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/// double median = dist.Median; // 5.0
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/// double var = dist.Variance; // 8.7395957193816862
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///
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/// // Cumulative distribution functions
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/// double cdf = dist.DistributionFunction(k: 2); // 0.19605133020527743
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/// double ccdf = dist.ComplementaryDistributionFunction(k: 2); // 0.80394866979472257
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///
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/// // Probability mass functions
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/// double pmf1 = dist.ProbabilityMassFunction(k: 4); // 0.054786846293416853
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/// double pmf2 = dist.ProbabilityMassFunction(k: 5); // 0.069908015870399909
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/// double pmf3 = dist.ProbabilityMassFunction(k: 6); // 0.0810932984096639
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/// double lpmf = dist.LogProbabilityMassFunction(k: 2); // -2.3927801721315989
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///
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/// // Quantile function
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/// int icdf1 = dist.InverseDistributionFunction(p: 0.17); // 2
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/// int icdf2 = dist.InverseDistributionFunction(p: 0.46); // 4
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/// int icdf3 = dist.InverseDistributionFunction(p: 0.87); // 8
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///
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/// // Hazard (failure rate) functions
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/// double hf = dist.HazardFunction(x: 4); // 0.10490438293398294
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/// double chf = dist.CumulativeHazardFunction(x: 4); // 0.64959916255036043
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///
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/// // String representation
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/// string str = dist.ToString(CultureInfo.InvariantCulture); // "NegativeBinomial(x; r = 7, p = 0.42)"
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/// </code>
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/// </example>
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///
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/// <seealso cref="BinomialDistribution"/>
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///
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[Serializable]
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public class NegativeBinomialDistribution : UnivariateDiscreteDistribution
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{
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int r; // number of failures
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double p; // success probability
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/// <summary>
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/// Creates a new Negative Binomial distribution.
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/// </summary>
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///
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/// <param name="failures">Number of failures <c>r</c>.</param>
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/// <param name="probability">Success probability in each experiment.</param>
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///
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public NegativeBinomialDistribution([PositiveInteger] int failures, [Unit] double probability)
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{
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if (failures <= 0)
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throw new ArgumentOutOfRangeException("failures");
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if (probability < 0 || probability > 1)
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throw new ArgumentOutOfRangeException("probability");
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this.r = failures;
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this.p = probability;
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}
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/// <summary>
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/// Gets the number of failures.
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/// </summary>
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///
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/// <value>The number of failures.</value>
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///
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public double NumberOfFailures
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{
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get { return r; }
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}
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/// <summary>
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/// Gets the probability of success.
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/// </summary>
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///
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/// <value>The probability of success in each experiment.</value>
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///
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public double ProbabilityOfSuccess
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{
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get { return p; }
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}
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/// <summary>
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/// Gets the mean for this distribution.
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/// </summary>
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///
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/// <value>The distribution's mean value.</value>
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///
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public override double Mean
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{
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get { return (p * r) / (1 - p); }
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set { throw new NotImplementedException();}
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}
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/// <summary>
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/// Gets the variance for this distribution.
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/// </summary>
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///
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/// <value>The distribution's variance.</value>
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///
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public override double Variance
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{
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get { return (p * r) / ((1 - p) * (1 - p)); }
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set { throw new NotImplementedException();}
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}
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/// <summary>
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/// Gets the entropy for this distribution.
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/// </summary>
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///
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/// <value>The distribution's entropy.</value>
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///
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public override double Entropy
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{
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get { throw new NotSupportedException(); }
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set { throw new NotImplementedException();}
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}
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/// <summary>
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/// Gets the support interval for this distribution.
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/// </summary>
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///
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/// <value>
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/// A <see cref="IntRange" /> containing
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/// the support interval for this distribution.
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/// </value>
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///
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public override IntRange Support
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{
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get { return new IntRange(0, Int32.MaxValue); }
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}
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/// <summary>
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/// Gets P( X<= k), the cumulative distribution function
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/// (cdf) for this distribution evaluated at point <c>k</c>.
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/// </summary>
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///
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/// <param name="k">A single point in the distribution range.</param>
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///
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/// <remarks>
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/// The Cumulative Distribution Function (CDF) describes the cumulative
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/// probability that a given value or any value smaller than it will occur.
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/// </remarks>
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///
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protected internal override double InnerDistributionFunction(int k)
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{
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return 1.0 - Beta.Incomplete(k + 1, r, 1 - p);
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}
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/// <summary>
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/// Gets the probability mass function (pmf) for
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/// this distribution evaluated at point <c>x</c>.
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/// </summary>
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///
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/// <param name="k">A single point in the distribution range.</param>
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///
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/// <returns>
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/// The probability of <c>k</c> occurring
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/// in the current distribution.
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/// </returns>
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///
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/// <remarks>
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/// The Probability Mass Function (PMF) describes the
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/// probability that a given value <c>x</c> will occur.
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/// </remarks>
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///
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protected internal override double InnerProbabilityMassFunction(int k)
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{
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return Special.Binomial(k + r - 1, r - 1) * Math.Pow(1 - p, k) * Math.Pow(p, r);
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}
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/// <summary>
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/// Gets the log-probability mass function (pmf) for
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/// this distribution evaluated at point <c>x</c>.
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/// </summary>
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///
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/// <param name="k">A single point in the distribution range.</param>
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///
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/// <returns>
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/// The logarithm of the probability of <c>x</c>
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/// occurring in the current distribution.
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/// </returns>
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///
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/// <remarks>
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/// The Probability Mass Function (PMF) describes the
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/// probability that a given value <c>k</c> will occur.
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/// </remarks>
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///
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protected internal override double InnerLogProbabilityMassFunction(int k)
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{
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return Special.LogBinomial(k + r - 1, r - 1) + k * Math.Log(1 - p) + r * Math.Log(p);
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}
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/// <summary>
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/// Creates a new object that is a copy of the current instance.
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/// </summary>
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///
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/// <returns>
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/// A new object that is a copy of this instance.
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/// </returns>
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///
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public override object Clone()
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{
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return new NegativeBinomialDistribution(r, p);
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}
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/// <summary>
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/// Fits the underlying distribution to a given set of observations.
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/// </summary>
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///
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/// <param name="observations">The array of observations to fit the model against. The array
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/// elements can be either of type double (for univariate data) or
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/// type double[] (for multivariate data).</param>
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/// <param name="weights">The weight vector containing the weight for each of the samples.</param>
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/// <param name="options">Optional arguments which may be used during fitting, such
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/// as regularization constants and additional parameters.</param>
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///
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public override void Fit(double[] observations, double[] weights, Fitting.IFittingOptions options)
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{
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throw new NotSupportedException();
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}
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/// <summary>
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/// Returns a <see cref="System.String"/> that represents this instance.
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/// </summary>
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///
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/// <returns>
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/// A <see cref="System.String"/> that represents this instance.
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/// </returns>
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///
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public override string ToString(string format, IFormatProvider formatProvider)
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{
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return String.Format(formatProvider, "NegativeBinomial(x; r = {0}, p = {1})",
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r.ToString(format, formatProvider),
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p.ToString(format, formatProvider));
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}
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}
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}
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