mirror of
https://github.com/hanzoai/jube-fork.git
synced 2026-10-30 18:33:33 +00:00
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.
389 lines
12 KiB
C#
389 lines
12 KiB
C#
// Accord Statistics Library
|
||
// The Accord.NET Framework
|
||
// http://accord-framework.net
|
||
//
|
||
// Copyright © César Souza, 2009-2017
|
||
// cesarsouza at gmail.com
|
||
//
|
||
// This library is free software; you can redistribute it and/or
|
||
// modify it under the terms of the GNU Lesser General Public
|
||
// License as published by the Free Software Foundation; either
|
||
// version 2.1 of the License, or (at your option) any later version.
|
||
//
|
||
// This library is distributed in the hope that it will be useful,
|
||
// but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
|
||
// Lesser General Public License for more details.
|
||
//
|
||
// You should have received a copy of the GNU Lesser General Public
|
||
// License along with this library; if not, write to the Free Software
|
||
// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||
//
|
||
|
||
namespace Accord.Statistics.Distributions.Univariate
|
||
{
|
||
using System;
|
||
using Accord.Math;
|
||
using Accord.Compat;
|
||
|
||
/// <summary>
|
||
/// Shift Log-Logistic distribution.
|
||
/// </summary>
|
||
///
|
||
/// <remarks>
|
||
/// <para>
|
||
/// The shifted log-logistic distribution is a probability distribution also known as
|
||
/// the generalized log-logistic or the three-parameter log-logistic distribution. It
|
||
/// has also been called the generalized logistic distribution, but this conflicts with
|
||
/// other uses of the term: see generalized logistic distribution.</para>
|
||
///
|
||
/// <para>
|
||
/// References:
|
||
/// <list type="bullet">
|
||
/// <item><description><a href="http://en.wikipedia.org/wiki/Shifted_log-logistic_distribution">
|
||
/// Wikipedia, The Free Encyclopedia. Shifted log-logistic distribution. Available on:
|
||
/// http://en.wikipedia.org/wiki/Shifted_log-logistic_distribution </a></description></item>
|
||
/// </list></para>
|
||
/// </remarks>
|
||
///
|
||
/// <example>
|
||
/// <para>
|
||
/// This examples shows how to create a Shifted Log-Logistic distribution,
|
||
/// compute some of its properties and generate a number of random samples
|
||
/// from it.</para>
|
||
///
|
||
/// <code>
|
||
/// // Create a LLD3 distribution with μ = 0.0, scale = 0.42, and shape = 0.1
|
||
/// var log = new ShiftedLogLogisticDistribution(location: 0, scale: 0.42, shape: 0.1);
|
||
///
|
||
/// double mean = log.Mean; // 0.069891101544818923
|
||
/// double median = log.Median; // 0.0
|
||
/// double mode = log.Mode; // -0.083441677069328604
|
||
/// double var = log.Variance; // 0.62447259946747213
|
||
///
|
||
/// double cdf = log.DistributionFunction(x: 1.4); // 0.94668863559417671
|
||
/// double pdf = log.ProbabilityDensityFunction(x: 1.4); // 0.090123683626808615
|
||
/// double lpdf = log.LogProbabilityDensityFunction(x: 1.4); // -2.4065722895662613
|
||
///
|
||
/// double ccdf = log.ComplementaryDistributionFunction(x: 1.4); // 0.053311364405823292
|
||
/// double icdf = log.InverseDistributionFunction(p: cdf); // 1.4000000037735139
|
||
///
|
||
/// double hf = log.HazardFunction(x: 1.4); // 1.6905154207038875
|
||
/// double chf = log.CumulativeHazardFunction(x: 1.4); // 2.9316057546685061
|
||
///
|
||
/// string str = log.ToString(CultureInfo.InvariantCulture); // LLD3(x; μ = 0, σ = 0.42, ξ = 0.1)
|
||
/// </code>
|
||
/// </example>
|
||
///
|
||
/// <seealso cref="LogisticDistribution"/>
|
||
/// <seealso cref="ParetoDistribution"/>
|
||
///
|
||
[Serializable]
|
||
public class ShiftedLogLogisticDistribution : UnivariateContinuousDistribution
|
||
{
|
||
|
||
// Distribution parameters
|
||
private double mu; // location μ (real)
|
||
private double sigma; // scale σ (positive)
|
||
private double ksi; // shape ξ (real)
|
||
|
||
/// <summary>
|
||
/// Constructs a Shifted Log-Logistic distribution
|
||
/// with zero location, unit scale, and zero shape.
|
||
/// </summary>
|
||
///
|
||
public ShiftedLogLogisticDistribution()
|
||
{
|
||
initialize(0, 1, 0);
|
||
}
|
||
|
||
/// <summary>
|
||
/// Constructs a Shifted Log-Logistic distribution
|
||
/// with the given location, unit scale and zero shape.
|
||
/// </summary>
|
||
///
|
||
/// <param name="location">The distribution's location value μ (mu).</param>
|
||
///
|
||
public ShiftedLogLogisticDistribution([Real] double location)
|
||
{
|
||
initialize(location, 1, 0);
|
||
}
|
||
|
||
/// <summary>
|
||
/// Constructs a Shifted Log-Logistic distribution
|
||
/// with the given location and scale and zero shape.
|
||
/// </summary>
|
||
///
|
||
/// <param name="location">The distribution's location value μ (mu).</param>
|
||
/// <param name="scale">The distribution's scale value σ (sigma).</param>
|
||
///
|
||
public ShiftedLogLogisticDistribution([Real] double location, [Positive] double scale)
|
||
{
|
||
if (scale <= 0)
|
||
throw new ArgumentOutOfRangeException("scale", "Scale must be positive.");
|
||
|
||
initialize(location, scale, 0);
|
||
}
|
||
|
||
/// <summary>
|
||
/// Constructs a Shifted Log-Logistic distribution
|
||
/// with the given location and scale and zero shape.
|
||
/// </summary>
|
||
///
|
||
/// <param name="location">The distribution's location value μ (mu).</param>
|
||
/// <param name="scale">The distribution's scale value s.</param>
|
||
/// <param name="shape">The distribution's shape value ξ (ksi).</param>
|
||
///
|
||
public ShiftedLogLogisticDistribution([Real] double location, [Positive] double scale, [Real] double shape)
|
||
{
|
||
if (scale <= 0)
|
||
throw new ArgumentOutOfRangeException("scale", "Scale must be positive.");
|
||
|
||
initialize(location, scale, shape);
|
||
}
|
||
|
||
|
||
|
||
/// <summary>
|
||
/// Gets the mean for this distribution.
|
||
/// </summary>
|
||
///
|
||
/// <value>
|
||
/// The distribution's mean value.
|
||
/// </value>
|
||
///
|
||
public override double Mean
|
||
{
|
||
get
|
||
{
|
||
if (ksi == 0)
|
||
return mu;
|
||
|
||
double b = Math.PI * ksi;
|
||
double a = sigma / ksi;
|
||
return mu + a * b * Special.Cosec(b) - a * 1;
|
||
}
|
||
set {} //Not Implemented.
|
||
}
|
||
|
||
/// <summary>
|
||
/// Gets the distribution's location value μ (mu).
|
||
/// </summary>
|
||
///
|
||
public double Location
|
||
{
|
||
get { return mu; }
|
||
}
|
||
|
||
/// <summary>
|
||
/// Gets the distribution's scale value (σ).
|
||
/// </summary>
|
||
///
|
||
public double Scale
|
||
{
|
||
get { return sigma; }
|
||
}
|
||
|
||
/// <summary>
|
||
/// Gets the distribution's shape value (ξ).
|
||
/// </summary>
|
||
///
|
||
public double Shape
|
||
{
|
||
get { return ksi; }
|
||
}
|
||
|
||
/// <summary>
|
||
/// Gets the median for this distribution.
|
||
/// </summary>
|
||
///
|
||
/// <value>
|
||
/// The distribution's median value.
|
||
/// </value>
|
||
///
|
||
public override double Median
|
||
{
|
||
get
|
||
{
|
||
Accord.Diagnostics.Debug.Assert(mu.IsEqual(base.Median, 1e-5));
|
||
return mu;
|
||
}
|
||
}
|
||
|
||
/// <summary>
|
||
/// Gets the variance for this distribution.
|
||
/// </summary>
|
||
///
|
||
/// <value>
|
||
/// The distribution's variance.
|
||
/// </value>
|
||
///
|
||
public override double Variance
|
||
{
|
||
get
|
||
{
|
||
if (ksi == 0)
|
||
{
|
||
// lim x->0 ((b^2)/(x^2))*(2*pi*x csc(2*pi*x) - (pi*x*csc(pi*x))^2)
|
||
// http://www.wolframalpha.com/input/?i=lim+x-%3E0++%28a+%2B+%28%28b%5E2%29%2F%28x%5E2%29%29*%282*pi*x+csc%282*pi*x%29+-+%28pi*x*csc%28pi*x%29%29%5E2%29%29
|
||
return sigma * sigma * Math.PI * Math.PI / 3.0;
|
||
}
|
||
else
|
||
{
|
||
double pb = Math.PI * ksi;
|
||
double a = (sigma * sigma) / (ksi * ksi);
|
||
double b = 2 * pb * Special.Cosec(2 * pb);
|
||
double c = pb * Special.Cosec(pb);
|
||
|
||
return a * (b - c * c);
|
||
}
|
||
}
|
||
set {} //Not Implemented.
|
||
}
|
||
|
||
/// <summary>
|
||
/// Gets the mode for this distribution.
|
||
/// </summary>
|
||
///
|
||
/// <value>
|
||
/// The distribution's mode value.
|
||
/// </value>
|
||
///
|
||
public override double Mode
|
||
{
|
||
get
|
||
{
|
||
if (ksi == 0)
|
||
return mu;
|
||
|
||
return mu + (sigma / ksi) * (Math.Pow((1 - ksi) / (1 + ksi), ksi) - 1);
|
||
}
|
||
set { } //Not Implemented.
|
||
}
|
||
|
||
/// <summary>
|
||
/// Not supported.
|
||
/// </summary>
|
||
///
|
||
public override double Entropy
|
||
{
|
||
get { throw new NotSupportedException(); }
|
||
set {} //Not Implemented.
|
||
}
|
||
|
||
/// <summary>
|
||
/// Gets the support interval for this distribution.
|
||
/// </summary>
|
||
///
|
||
/// <value>
|
||
/// A <see cref="DoubleRange" /> containing
|
||
/// the support interval for this distribution.
|
||
/// </value>
|
||
///
|
||
public override DoubleRange Support
|
||
{
|
||
get
|
||
{
|
||
if (ksi > 0)
|
||
return new DoubleRange(mu - sigma / ksi, Double.PositiveInfinity);
|
||
|
||
if (ksi < 0)
|
||
return new DoubleRange(Double.NegativeInfinity, mu - sigma / ksi);
|
||
|
||
// if (ksi == 0)
|
||
return new DoubleRange(Double.NegativeInfinity, Double.PositiveInfinity);
|
||
}
|
||
set {} //Not Implemented.
|
||
}
|
||
|
||
|
||
/// <summary>
|
||
/// Gets the cumulative distribution function (cdf) for
|
||
/// this distribution evaluated at point <c>x</c>.
|
||
/// </summary>
|
||
///
|
||
/// <param name="x">A single point in the distribution range.</param>
|
||
///
|
||
protected internal override double InnerDistributionFunction(double x)
|
||
{
|
||
if (ksi > 0 && x < mu - sigma / ksi)
|
||
return 0;
|
||
|
||
double z = (x - mu) / sigma;
|
||
|
||
if (ksi == 0)
|
||
return 1 / (1 + Math.Exp(-z));
|
||
|
||
return 1 / (1 + Math.Pow(1 + ksi * z, -1 / ksi));
|
||
}
|
||
|
||
/// <summary>
|
||
/// Gets the probability density function (pdf) for
|
||
/// this distribution evaluated at point <c>x</c>.
|
||
/// </summary>
|
||
///
|
||
/// <param name="x">A single point in the distribution range.</param>
|
||
///
|
||
/// <returns>
|
||
/// The probability of <c>x</c> occurring
|
||
/// in the current distribution.
|
||
/// </returns>
|
||
///
|
||
protected internal override double InnerProbabilityDensityFunction(double x)
|
||
{
|
||
double z = (x - mu) / sigma;
|
||
|
||
double a, b;
|
||
|
||
if (ksi == 0)
|
||
{
|
||
a = Math.Exp(-z);
|
||
b = (1 + a);
|
||
}
|
||
else
|
||
{
|
||
a = Math.Pow(1 + ksi * z, -1 / ksi - 1);
|
||
b = 1 + Math.Pow(1 + ksi * z, -1 / ksi);
|
||
}
|
||
|
||
return a / (sigma * b * b);
|
||
}
|
||
|
||
/// <summary>
|
||
/// Creates a new object that is a copy of the current instance.
|
||
/// </summary>
|
||
/// <returns>
|
||
/// A new object that is a copy of this instance.
|
||
/// </returns>
|
||
///
|
||
public override object Clone()
|
||
{
|
||
return new ShiftedLogLogisticDistribution(mu, sigma, ksi);
|
||
}
|
||
|
||
/// <summary>
|
||
/// Returns a <see cref="System.String"/> that represents this instance.
|
||
/// </summary>
|
||
///
|
||
/// <returns>
|
||
/// A <see cref="System.String"/> that represents this instance.
|
||
/// </returns>
|
||
///
|
||
public override string ToString(string format, IFormatProvider formatProvider)
|
||
{
|
||
return String.Format(formatProvider, "LLD3(x; μ = {0}, σ = {1}, ξ = {2})",
|
||
mu.ToString(format, formatProvider),
|
||
sigma.ToString(format, formatProvider),
|
||
ksi.ToString(format, formatProvider));
|
||
}
|
||
|
||
|
||
private void initialize(double mean, double scale, double shape)
|
||
{
|
||
this.mu = mean;
|
||
this.sigma = scale;
|
||
this.ksi = shape;
|
||
}
|
||
}
|
||
}
|