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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.
255 lines
7.9 KiB
C#
255 lines
7.9 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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/// Hyperbolic Secant 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 theory and statistics, the hyperbolic secant distribution is
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/// a continuous probability distribution whose probability density function and
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/// characteristic function are proportional to the hyperbolic secant function.
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/// The hyperbolic secant function is equivalent to the inverse hyperbolic cosine,
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/// and thus this distribution is also called the inverse-cosh distribution.</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/Sech_distribution">
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/// Wikipedia, The Free Encyclopedia. Hyperbolic secant distribution. Available on:
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/// http://en.wikipedia.org/wiki/Sech_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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/// This examples shows how to create a Sech distribution,
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/// compute some of its properties and generate a number of
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/// random samples from it.</para>
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///
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/// <code>
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/// // Create a new hyperbolic secant distribution
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/// var sech = new HyperbolicSecantDistribution();
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///
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/// double mean = sech.Mean; // 0.0
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/// double median = sech.Median; // 0.0
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/// double mode = sech.Mode; // 0.0
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/// double var = sech.Variance; // 1.0
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///
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/// double cdf = sech.DistributionFunction(x: 1.4); // 0.92968538268895873
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/// double pdf = sech.ProbabilityDensityFunction(x: 1.4); // 0.10955386512899701
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/// double lpdf = sech.LogProbabilityDensityFunction(x: 1.4); // -2.2113389316917877
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///
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/// double ccdf = sech.ComplementaryDistributionFunction(x: 1.4); // 0.070314617311041272
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/// double icdf = sech.InverseDistributionFunction(p: cdf); // 1.40
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///
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/// double hf = sech.HazardFunction(x: 1.4); // 1.5580524977385339
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///
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/// string str = sech.ToString(); // Sech(x)
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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 HyperbolicSecantDistribution : UnivariateContinuousDistribution
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{
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/// <summary>
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/// Constructs a Hyperbolic Secant (Sech) distribution.
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/// </summary>
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///
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public HyperbolicSecantDistribution()
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{
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}
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/// <summary>
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/// Gets the mean for this distribution (always zero).
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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 { return 0; }
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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 (always zero).
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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 { return 0; }
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}
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/// <summary>
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/// Gets the variance for this distribution (always one).
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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 { return 1; }
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set {} //Not Implemented.
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}
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/// <summary>
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/// Gets the Standard Deviation (the square root of
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/// the variance) for the current distribution.
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/// </summary>
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///
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/// <value>
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/// The distribution's standard deviation.
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/// </value>
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///
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public override double StandardDeviation
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{
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get { return 1; }
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}
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/// <summary>
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/// Gets the mode for this distribution (always zero).
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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 0; }
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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 (-inf, +inf).
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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.NegativeInfinity, 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>
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/// The distribution's entropy.
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/// </value>
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///
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public override double Entropy
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{
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get { return (4.0 / Math.PI) * Constants.Catalan; }
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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 angle = Math.Atan(Math.Exp(x * Math.PI / 2.0));
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return 2 * angle / Math.PI;
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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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return 0.5 * Special.Sech(x * (Math.PI / 2.0));
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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 HyperbolicSecantDistribution();
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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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/// <param name="format">The format.</param>
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/// <param name="formatProvider">The format provider.</param>
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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, "Sech(x)");
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}
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}
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}
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