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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.
246 lines
8.3 KiB
C#
246 lines
8.3 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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/// U-quadratic 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 U-quadratic distribution is a continuous
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/// probability distribution defined by a unique quadratic function with lower limit a
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/// and upper limit b. This distribution is a useful model for symmetric bimodal processes.
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/// Other continuous distributions allow more flexibility, in terms of relaxing the symmetry
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/// and the quadratic shape of the density function, which are enforced in the U-quadratic
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/// distribution - e.g., Beta distribution, Gamma distribution, etc. </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/U-quadratic_distribution">
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/// Wikipedia, The Free Encyclopedia. U-quadratic distribution. Available on:
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/// http://en.wikipedia.org/wiki/U-quadratic_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 U-quadratic distribution given its two parameters: </para>
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///
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/// <code>
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/// // Create a new U-quadratic distribution with values
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/// var u2 = new UQuadraticDistribution(a: 0.42, b: 4.2);
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///
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/// double mean = u2.Mean; // 2.3100000000000001
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/// double median = u2.Median; // 2.3100000000000001
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/// double mode = u2.Mode; // 0.8099060089153145
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/// double var = u2.Variance; // 2.1432600000000002
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///
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/// double cdf = u2.DistributionFunction(x: 1.4); // 0.44419041812731797
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/// double pdf = u2.ProbabilityDensityFunction(x: 1.4); // 0.18398763254730335
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/// double lpdf = u2.LogProbabilityDensityFunction(x: 1.4); // -1.6928867380489712
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///
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/// double ccdf = u2.ComplementaryDistributionFunction(x: 1.4); // 0.55580958187268203
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/// double icdf = u2.InverseDistributionFunction(p: cdf); // 1.3999998213768274
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///
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/// double hf = u2.HazardFunction(x: 1.4); // 0.3310263776442936
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/// double chf = u2.CumulativeHazardFunction(x: 1.4); // 0.58732952203701494
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///
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/// string str = u2.ToString(CultureInfo.InvariantCulture); // "UQuadratic(x; a = 0.42, b = 4.2)"
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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 UQuadraticDistribution : UnivariateContinuousDistribution
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{
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// Distribution parameters
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double a;
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double b;
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double alpha;
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double beta;
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/// <summary>
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/// Constructs a new U-quadratic distribution.
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/// </summary>
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///
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/// <param name="a">Parameter a.</param>
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/// <param name="b">Parameter b.</param>
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///
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public UQuadraticDistribution([Nonnegative] double a, [Positive] double b)
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{
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if (b < a)
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{
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throw new ArgumentOutOfRangeException("b",
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"Parameter b must be equal to or greater than parameter a.");
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}
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this.a = a;
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this.b = b;
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this.alpha = 12 / Math.Pow(b - a, 3);
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this.beta = (b + a) / 2;
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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>
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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 (a + b) / 2.0d; }
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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 { return (a + b) / 2.0d; }
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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 { return (3.0d / 20.0d) * Math.Pow(b - a, 2.0d); }
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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(a, b); }
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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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return (alpha / 3) * (Math.Pow(x - beta, 3) + Math.Pow(beta - a, 3));
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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 alpha * Math.Pow(x - beta, 2);
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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 UQuadraticDistribution(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, "U-Quadratic(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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