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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.
275 lines
9.1 KiB
C#
275 lines
9.1 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 AForge;
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/// <summary>
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/// Gompertz 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 Gompertz distribution is a continuous probability distribution. The
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/// Gompertz distribution is often applied to describe the distribution of
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/// adult lifespans by demographers and actuaries. Related fields of science
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/// such as biology and gerontology also considered the Gompertz distribution
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/// for the analysis of survival. More recently, computer scientists have also
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/// started to model the failure rates of computer codes by the Gompertz
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/// distribution. In marketing science, it has been used as an individual-level
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/// model of customer lifetime.</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/Gamma_distribution">
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/// Wikipedia, The Free Encyclopedia. Gompertz distribution. Available on:
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/// http://en.wikipedia.org/wiki/Gompertz_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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/// <para>
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/// The following example shows how to construct a Gompertz
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/// distribution with <c>η = 4.2</c> and <c>b = 1.1</c>.</para>
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///
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/// <code>
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/// // Create a new Gompertz distribution with η = 4.2 and b = 1.1
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/// GompertzDistribution dist = new GompertzDistribution(eta: 4.2, b: 1.1);
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///
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/// // Common measures
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/// double median = dist.Median; // 0.13886469671401389
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///
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/// // Cumulative distribution functions
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/// double cdf = dist.DistributionFunction(x: 0.27); // 0.76599768199799145
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/// double ccdf = dist.ComplementaryDistributionFunction(x: 0.27); // 0.23400231800200855
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/// double icdf = dist.InverseDistributionFunction(p: cdf); // 0.26999999999766749
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///
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/// // Probability density functions
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/// double pdf = dist.ProbabilityDensityFunction(x: 0.27); // 1.4549484164912097
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/// double lpdf = dist.LogProbabilityDensityFunction(x: 0.27); // 0.37497044741163688
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///
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/// // Hazard (failure rate) functions
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/// double hf = dist.HazardFunction(x: 0.27); // 6.2176666834502088
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/// double chf = dist.CumulativeHazardFunction(x: 0.27); // 1.4524242576820101
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///
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/// // String representation
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/// string str = dist.ToString(CultureInfo.InvariantCulture); // "Gompertz(x; η = 4.2, b = 1.1)"
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/// </code>
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/// </example>
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///
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public class GompertzDistribution : UnivariateContinuousDistribution
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{
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private double eta;
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private double b;
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/// <summary>
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/// Initializes a new instance of the <see cref="GompertzDistribution"/> class.
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/// </summary>
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///
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/// <param name="eta">The shape parameter <c>η</c>.</param>
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/// <param name="b">The scale parameter <c>b</c>.</param>
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///
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public GompertzDistribution([Positive] double eta, [Positive] double b)
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{
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if (eta <= 0)
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throw new ArgumentOutOfRangeException("eta", "The shape eta must be positive.");
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if (b <= 0)
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throw new ArgumentOutOfRangeException("b", "The scale b must be positive.");
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this.eta = eta;
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this.b = b;
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}
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/// <summary>
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/// Not supported.
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/// </summary>
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///
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public override double Mean
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{
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get { throw new NotSupportedException(); }
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set {} //Not Implemented.
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}
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/// <summary>
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/// Not supported.
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/// </summary>
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///
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public override double Variance
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{
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get { throw new NotSupportedException(); }
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set {} //Not Implemented.
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}
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/// <summary>
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/// Gets the mode for this distribution.
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/// </summary>
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///
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/// <value>
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/// The distribution's mode value.
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/// </value>
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///
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public override double Mode
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{
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get
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{
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if (eta >= 1)
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return 0;
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return (1 / b) * Math.Log(1 / eta);
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}
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set { } //Not Implemented.
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}
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/// <summary>
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/// Gets the median for this distribution.
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/// </summary>
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///
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/// <value>
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/// The distribution's median value.
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/// </value>
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///
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public override double Median
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{
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get
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{
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return (1.0 / b) * Math.Log((-1 / eta) * Math.Log(0.5) + 1);
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}
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}
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/// <summary>
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/// Not supported.
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/// </summary>
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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 {} //Not Implemented.
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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="DoubleRange" /> 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 DoubleRange Support
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{
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get { return new DoubleRange(0, Double.PositiveInfinity); }
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set {} //Not Implemented.
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}
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/// <summary>
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/// Gets the cumulative distribution function (cdf) 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="x">A single point in the distribution range.</param>
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///
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protected internal override double InnerDistributionFunction(double x)
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{
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double ebx = Math.Exp(b * x);
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double cdf = 1.0 - Math.Exp(-eta * (ebx - 1.0));
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return cdf;
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}
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/// <summary>
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/// Gets the probability density function (pdf) 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="x">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>x</c> occurring
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/// in the current distribution.
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/// </returns>
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///
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protected internal override double InnerProbabilityDensityFunction(double x)
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{
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double a1 = b * eta * Math.Exp(eta);
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double a2 = Math.Exp(b * x);
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double a3 = Math.Exp(-eta * Math.Exp(b * x));
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return a1 * a2 * a3;
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}
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/// <summary>
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/// Gets the log-probability density function (pdf) 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="x">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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protected internal override double InnerLogProbabilityDensityFunction(double x)
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{
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double a1 = Math.Log(b * eta) + eta;
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double a2 = b * x;
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double a3 = -eta * Math.Exp(b * x);
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return a1 + a2 + a3;
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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 GompertzDistribution(eta, b);
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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, "Gompertz(x; η = {0}, b = {1})",
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eta.ToString(format, formatProvider),
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b.ToString(format, formatProvider));
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}
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}
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}
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