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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.
307 lines
10 KiB
C#
307 lines
10 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 © Ashley Messer, 2014
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// glyphard 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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/// Kumaraswamy distribution.
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/// </summary>
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///
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/// <remarks>
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/// <para>
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/// In probability and statistics, the Kumaraswamy's double bounded distribution is a
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/// family of continuous probability distributions defined on the interval [0,1] differing
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/// in the values of their two non-negative shape parameters, a and b.
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/// It is similar to the Beta distribution, but much simpler to use especially in simulation
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/// studies due to the simple closed form of both its probability density function and
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/// cumulative distribution function. This distribution was originally proposed by Poondi
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/// Kumaraswamy for variables that are lower and upper bounded.</para>
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///
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/// <para>
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/// A good example of the use of the Kumaraswamy distribution is the storage volume of a
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/// reservoir of capacity z<sub>max</sub> whose upper bound is z<sub>max</sub> and lower
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/// bound is 0 (Fletcher and Ponnambalam, 1996).</para>
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///
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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/Kumaraswamy_distribution">
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/// Wikipedia, The Free Encyclopedia. Kumaraswamy distribution. Available on:
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/// http://en.wikipedia.org/wiki/Kumaraswamy_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 create and test the main characteristics
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/// of an Kumaraswamy distribution given its two non-negative shape parameters: </para>
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///
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/// <code>
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/// // Create a new Kumaraswamy distribution with shape (4,2)
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/// var kumaraswamy = new KumaraswamyDistribution(a: 4, b: 2);
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///
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/// double mean = kumaraswamy.Mean; // 0.71111111111111114
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/// double median = kumaraswamy.Median; // 0.73566031573423674
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/// double mode = kumaraswamy.Mode; // 0.80910671157022118
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/// double var = kumaraswamy.Variance; // 0.027654320987654302
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///
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/// double cdf = kumaraswamy.DistributionFunction(x: 0.4); // 0.050544639999999919
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/// double pdf = kumaraswamy.ProbabilityDensityFunction(x: 0.4); // 0.49889280000000014
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/// double lpdf = kumaraswamy.LogProbabilityDensityFunction(x: 0.4); // -0.69536403596913343
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///
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/// double ccdf = kumaraswamy.ComplementaryDistributionFunction(x: 0.4); // 0.94945536000000008
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/// double icdf = kumaraswamy.InverseDistributionFunction(p: cdf); // 0.40000011480618253
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///
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/// double hf = kumaraswamy.HazardFunction(x: 0.4); // 0.52545155993431869
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/// double chf = kumaraswamy.CumulativeHazardFunction(x: 0.4); // 0.051866764053008864
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///
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/// string str = kumaraswamy.ToString(CultureInfo.InvariantCulture); // Kumaraswamy(x; a = 4, b = 2)
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/// </code>
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/// </example>
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///
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[Serializable]
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public class KumaraswamyDistribution : UnivariateContinuousDistribution
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{
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double a;
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double b;
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/// <summary>
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/// Constructs a new Kumaraswamy's double bounded distribution with
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/// the given two non-negative shape parameters <c>a</c> and <c>b</c>.
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/// </summary>
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///
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/// <param name="a">The distribution's non-negative shape parameter a.</param>
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/// <param name="b">The distribution's non-negative shape parameter b.</param>
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///
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public KumaraswamyDistribution([Positive] double a, [Positive] double b)
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{
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if (a <= 0)
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throw new ArgumentOutOfRangeException("a", "The shape parameter a must be positive.");
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if (b < 0)
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throw new ArgumentOutOfRangeException("b", "The shape parameter b must be positive.");
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this.a = a;
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this.b = b;
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}
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/// <summary>
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/// Gets the distribution's non-negative shape parameter a.
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/// </summary>
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///
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public double A { get { return a; } }
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/// <summary>
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/// Gets the distribution's non-negative shape parameter b.
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/// </summary>
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///
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public double B { get { return b; } }
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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>
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/// The distribution's mean value.
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/// </value>
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///
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public override double Mean
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{
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get
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{
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double num = b * Gamma.Function(1 + (1 / a)) * Gamma.Function(b);
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double den = Gamma.Function(1 + (1 / a) + b);
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return num / den;
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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 variance for this distribution.
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/// </summary>
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///
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/// <value>
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/// The distribution's variance.
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/// </value>
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///
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public override double Variance
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{
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get
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{
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double alpha = momentGeneratingFunction(2, a, b);
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double beta = Math.Pow(momentGeneratingFunction(1, a, b), 2);
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return alpha - beta;
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}
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set {} //Not Implemented.
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}
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private static double momentGeneratingFunction(int n, double a, double b)
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{
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return (b * Beta.Function(1.0d + ((double)n) / a, b));
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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 Math.Pow(1 - Math.Pow(2, -1 / b), 1 / a);
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}
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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 ((a >= 1) && (b >= 1) && (a != 1 && b != 1))
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{
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double num = a - 1;
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double den = a * b - 1;
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return Math.Pow(num / den, 1 / a);
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}
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return Double.NaN;
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}
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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 Entropy
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{
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get { return double.NaN; }
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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, 1); }
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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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/// 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(double x)
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{
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double xa = Math.Pow(x, a);
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return 1 - Math.Pow(1 - xa, b);
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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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protected internal override double InnerProbabilityDensityFunction(double x)
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{
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return a * b * Math.Pow(x, a - 1) * Math.Pow(1 - Math.Pow(x, a), b - 1);
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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 KumaraswamyDistribution(this.a, this.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, "Kumaraswamy(x; a = {0}, b = {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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