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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.
295 lines
11 KiB
C#
295 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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/// Inverse Gamma 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 inverse gamma distribution is a two-parameter family of continuous probability
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/// distributions on the positive real line, which is the distribution of the reciprocal
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/// of a variable distributed according to the gamma distribution. Perhaps the chief use
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/// of the inverse gamma distribution is in Bayesian statistics, where it serves as the
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/// conjugate prior of the variance of a normal distribution. However, it is common among
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/// Bayesians to consider an alternative parameterization of the normal distribution in
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/// terms of the precision, defined as the reciprocal of the variance, which allows the
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/// gamma distribution to be used directly as a conjugate prior.</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/Inverse-gamma_distribution">
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/// Wikipedia, The Free Encyclopedia. Inverse Gamma Distribution.
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/// Available from: http://en.wikipedia.org/wiki/Inverse-gamma_distribution </a></description></item>
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/// <item><description><a href="http://www.johndcook.com/inverse gamma.pdf">
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/// John D. Cook. (2008). The Inverse Gamma 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 inverse Gamma distribution with α = 0.42 and β = 0.5
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/// var invGamma = new InverseGammaDistribution(shape: 0.42, scale: 0.5);
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///
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/// // Common measures
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/// double mean = invGamma.Mean; // -0.86206896551724133
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/// double median = invGamma.Median; // 3.1072323347401709
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/// double var = invGamma.Variance; // -0.47035626665061164
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///
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/// // Cumulative distribution functions
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/// double cdf = invGamma.DistributionFunction(x: 0.27); // 0.042243552114989695
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/// double ccdf = invGamma.ComplementaryDistributionFunction(x: 0.27); // 0.95775644788501035
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/// double icdf = invGamma.InverseDistributionFunction(p: cdf); // 0.26999994629410995
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///
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/// // Probability density functions
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/// double pdf = invGamma.ProbabilityDensityFunction(x: 0.27); // 0.35679850067181362
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/// double lpdf = invGamma.LogProbabilityDensityFunction(x: 0.27); // -1.0305840804381006
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///
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/// // Hazard (failure rate) functions
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/// double hf = invGamma.HazardFunction(x: 0.27); // 0.3725357333377633
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/// double chf = invGamma.CumulativeHazardFunction(x: 0.27); // 0.043161763098266373
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///
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/// // String representation
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/// string str = invGamma.ToString(); // Γ^(-1)(x; α = 0.42, β = 0.5)
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/// </code>
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/// </example>
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///
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/// <seealso cref="GammaDistribution"/>
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///
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[Serializable]
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public class InverseGammaDistribution : UnivariateContinuousDistribution
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{
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double a;
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double b;
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double constant;
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/// <summary>
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/// Creates a new Inverse Gamma Distribution.
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/// </summary>
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///
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/// <param name="shape">The shape parameter α (alpha).</param>
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/// <param name="scale">The scale parameter β (beta).</param>
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///
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public InverseGammaDistribution([Positive] double shape, [Positive] double scale)
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{
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if (shape <= 0)
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throw new ArgumentOutOfRangeException("shape");
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if (scale <= 0)
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throw new ArgumentOutOfRangeException("scale");
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this.a = shape;
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this.b = scale;
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this.constant = Math.Pow(b, a) / Gamma.Function(a);
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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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/// <remarks>
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/// In the Inverse Gamma distribution, the Mean is given as b / (a - 1).
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/// </remarks>
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///
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public override double Mean
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{
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get { return b / (a - 1); }
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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 { return b / (a + 1); }
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set { } //Not Implemented.
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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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/// <remarks>
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/// In the Inverse Gamma distribution, the Variance is given as b² / ((a - 1)² * (a - 2)).
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/// </remarks>
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///
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public override double Variance
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{
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get { return (b * b) / ((a - 1) * (a - 1) * (a - 2)); }
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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(Double.Epsilon, Double.PositiveInfinity); }
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set {} //Not Implemented.
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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 { return a + Math.Log(b * Gamma.Function(a)) - (1 + a) * Gamma.Digamma(a); }
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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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/// <remarks>
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/// <para>
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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.</para>
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///
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/// <para>
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/// In the Inverse Gamma CDF is computed in terms of the <see cref="Gamma.UpperIncomplete">
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/// Upper Incomplete Regularized Gamma Function Q</see> as CDF(x) = Q(a, b / x).</para>
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/// </remarks>
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///
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/// <example>
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/// See <see cref="InverseGammaDistribution"/>.
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/// </example>
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///
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protected internal override double InnerDistributionFunction(double x)
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{
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return Gamma.UpperIncomplete(a, b / x);
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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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/// <remarks>
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/// The Probability Density Function (PDF) 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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/// <example>
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/// See <see cref="InverseGammaDistribution"/>.
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/// </example>
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///
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protected internal override double InnerProbabilityDensityFunction(double x)
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{
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return constant * Math.Pow(x, -a - 1) * Math.Exp(-b / x);
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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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/// <remarks>
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/// The Probability Density Function (PDF) 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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/// <example>
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/// See <see cref="InverseGammaDistribution"/>.
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/// </example>
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///
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protected internal override double InnerLogProbabilityDensityFunction(double x)
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{
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double lnx = Math.Log(x);
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return Math.Log(constant) + (-a - 1) * lnx + (-b / x);
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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 InverseGammaDistribution(a, 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, "Γ^(-1)(x; α = {0}, β = {1})",
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a.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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