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.
327 lines
11 KiB
C#
327 lines
11 KiB
C#
// Accord Statistics Library
|
||
// The Accord.NET Framework
|
||
// http://accord-framework.net
|
||
//
|
||
// Copyright © Ashley Messer, 2014
|
||
// glyphard 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>
|
||
/// Beta prime distribution.
|
||
/// </summary>
|
||
///
|
||
/// <remarks>
|
||
/// <para>
|
||
/// In probability theory and statistics, the beta prime distribution (also known as inverted
|
||
/// beta distribution or beta distribution of the second kind) is an absolutely continuous
|
||
/// probability distribution defined for <c>x > 0</c> with two parameters α and β, having the
|
||
/// probability density function:</para>
|
||
///
|
||
/// <code>
|
||
/// x^(α-1) (1+x)^(-α-β)
|
||
/// f(x) = --------------------
|
||
/// B(α,β)
|
||
/// </code>
|
||
///
|
||
/// <para>
|
||
/// where B is the <see cref="Beta">Beta function</see>. While the related beta distribution is
|
||
/// the conjugate prior distribution of the parameter of a <see cref="BernoulliDistribution">Bernoulli
|
||
/// distribution</see> expressed as a probability, the beta prime distribution is the conjugate prior
|
||
/// distribution of the parameter of a Bernoulli distribution expressed in odds. The distribution is
|
||
/// a Pearson type VI distribution.</para>
|
||
///
|
||
/// <para>
|
||
/// References:
|
||
/// <list type="bullet">
|
||
/// <item><description><a href="http://en.wikipedia.org/wiki/Beta_prime_distribution">
|
||
/// Wikipedia, The Free Encyclopedia. Beta Prime distribution. Available on:
|
||
/// http://en.wikipedia.org/wiki/Beta_prime_distribution </a></description></item>
|
||
/// </list></para>
|
||
/// </remarks>
|
||
///
|
||
/// <example>
|
||
/// <para>
|
||
/// The following example shows how to create and test the main characteristics
|
||
/// of an Beta prime distribution given its two non-negative shape parameters: </para>
|
||
///
|
||
/// <code>
|
||
/// // Create a new Beta-Prime distribution with shape (4,2)
|
||
/// var betaPrime = new BetaPrimeDistribution(alpha: 4, beta: 2);
|
||
///
|
||
/// double mean = betaPrime.Mean; // 4.0
|
||
/// double median = betaPrime.Median; // 2.1866398762435981
|
||
/// double mode = betaPrime.Mode; // 1.0
|
||
/// double var = betaPrime.Variance; // +inf
|
||
///
|
||
/// double cdf = betaPrime.DistributionFunction(x: 0.4); // 0.02570357589099781
|
||
/// double pdf = betaPrime.ProbabilityDensityFunction(x: 0.4); // 0.16999719504628183
|
||
/// double lpdf = betaPrime.LogProbabilityDensityFunction(x: 0.4); // -1.7719733417957513
|
||
///
|
||
/// double ccdf = betaPrime.ComplementaryDistributionFunction(x: 0.4); // 0.97429642410900219
|
||
/// double icdf = betaPrime.InverseDistributionFunction(p: cdf); // 0.39999982363709291
|
||
///
|
||
/// double hf = betaPrime.HazardFunction(x: 0.4); // 0.17448200654307533
|
||
/// double chf = betaPrime.CumulativeHazardFunction(x: 0.4); // 0.026039684773113869
|
||
///
|
||
/// string str = betaPrime.ToString(CultureInfo.InvariantCulture); // BetaPrime(x; α = 4, β = 2)
|
||
/// </code>
|
||
/// </example>
|
||
///
|
||
[Serializable]
|
||
public class BetaPrimeDistribution : UnivariateContinuousDistribution
|
||
{
|
||
|
||
// Distribution parameters
|
||
double alpha; // shape (α)
|
||
double beta; // shape (β)
|
||
|
||
/// <summary>
|
||
/// Constructs a new Beta-Prime distribution with the given
|
||
/// two non-negative shape parameters <c>a</c> and <c>b</c>.
|
||
/// </summary>
|
||
///
|
||
/// <param name="alpha">The distribution's non-negative shape parameter a.</param>
|
||
/// <param name="beta">The distribution's non-negative shape parameter b.</param>
|
||
///
|
||
public BetaPrimeDistribution([Positive] double alpha, [Positive] double beta)
|
||
{
|
||
if (alpha <= 0)
|
||
throw new ArgumentOutOfRangeException("alpha", "The shape parameter alpha must be positive.");
|
||
|
||
if (beta < 0)
|
||
throw new ArgumentOutOfRangeException("beta", "The shape parameter beta must be positive.");
|
||
|
||
|
||
this.alpha = alpha;
|
||
this.beta = beta;
|
||
}
|
||
|
||
/// <summary>
|
||
/// Gets the distribution's non-negative shape parameter a.
|
||
/// </summary>
|
||
///
|
||
public double Alpha
|
||
{
|
||
get { return alpha; }
|
||
}
|
||
|
||
/// <summary>
|
||
/// Gets the distribution's non-negative shape parameter b.
|
||
/// </summary>
|
||
///
|
||
public double Beta
|
||
{
|
||
get { return beta; }
|
||
}
|
||
|
||
/// <summary>
|
||
/// Gets the mean for this distribution.
|
||
/// </summary>
|
||
///
|
||
/// <value>
|
||
/// The distribution's mean value.
|
||
/// </value>
|
||
///
|
||
public override double Mean
|
||
{
|
||
get
|
||
{
|
||
if (beta > 1)
|
||
return alpha / (beta - 1);
|
||
|
||
return Double.PositiveInfinity;
|
||
}
|
||
set { throw new NotImplementedException();}
|
||
}
|
||
|
||
/// <summary>
|
||
/// Gets the mode for this distribution.
|
||
/// </summary>
|
||
///
|
||
/// <value>
|
||
/// The distribution's mode value.
|
||
/// </value>
|
||
///
|
||
public override double Mode
|
||
{
|
||
get
|
||
{
|
||
if (alpha >= 1)
|
||
return (alpha - 1) / (beta + 1);
|
||
|
||
return 0.0;
|
||
}
|
||
set { throw new NotImplementedException();}
|
||
}
|
||
|
||
/// <summary>
|
||
/// Gets the variance for this distribution.
|
||
/// </summary>
|
||
///
|
||
/// <value>
|
||
/// The distribution's variance.
|
||
/// </value>
|
||
///
|
||
public override double Variance
|
||
{
|
||
get
|
||
{
|
||
if (beta > 2.0)
|
||
{
|
||
double num = alpha * (alpha + beta - 1);
|
||
double den = (beta - 2) * Math.Pow(beta - 1, 2);
|
||
return num / den;
|
||
}
|
||
else if (beta > 1.0)
|
||
{
|
||
return Double.PositiveInfinity;
|
||
}
|
||
|
||
return double.NaN;
|
||
}
|
||
set { throw new NotImplementedException();}
|
||
}
|
||
|
||
/// <summary>
|
||
/// Not supported.
|
||
/// </summary>
|
||
///
|
||
public override double Entropy
|
||
{
|
||
get { return double.NaN; }
|
||
set { throw new NotImplementedException();}
|
||
}
|
||
|
||
/// <summary>
|
||
/// Gets the support interval for this distribution, which
|
||
/// for the Beta- Prime distribution ranges from 0 to all
|
||
/// positive numbers.
|
||
/// </summary>
|
||
///
|
||
/// <value>
|
||
/// A <see cref="DoubleRange" /> containing
|
||
/// the support interval for this distribution.
|
||
/// </value>
|
||
///
|
||
public override DoubleRange Support
|
||
{
|
||
get { return new DoubleRange(0, Double.PositiveInfinity); }
|
||
set { throw new NotImplementedException();}
|
||
}
|
||
|
||
/// <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>
|
||
///
|
||
/// <remarks>
|
||
/// The Cumulative Distribution Function (CDF) describes the cumulative
|
||
/// probability that a given value or any value smaller than it will occur.
|
||
/// </remarks>
|
||
///
|
||
protected internal override double InnerDistributionFunction([Positive] double x)
|
||
{
|
||
return Accord.Math.Beta.Incomplete(alpha, beta, x / (1 + x));
|
||
}
|
||
|
||
/// <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>
|
||
///
|
||
/// <remarks>
|
||
/// The Probability Density Function (PDF) describes the
|
||
/// probability that a given value <c>x</c> will occur.
|
||
/// </remarks>
|
||
///
|
||
protected internal override double InnerProbabilityDensityFunction([Positive] double x)
|
||
{
|
||
double num = Math.Pow(x, alpha - 1) * Math.Pow(1 + x, -alpha - beta);
|
||
double den = Accord.Math.Beta.Function(alpha, beta);
|
||
return num / den;
|
||
}
|
||
|
||
/// <summary>
|
||
/// Gets the log-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 logarithm of the probability of <c>x</c>
|
||
/// occurring in the current distribution.
|
||
/// </returns>
|
||
///
|
||
/// <remarks>
|
||
/// The Probability Density Function (PDF) describes the
|
||
/// probability that a given value <c>x</c> will occur.
|
||
/// </remarks>
|
||
///
|
||
protected internal override double InnerLogProbabilityDensityFunction([Positive] double x)
|
||
{
|
||
double num = (alpha - 1) * Math.Log(x) + (-alpha - beta) * Math.Log(1 + x);
|
||
double den = Accord.Math.Beta.Log(alpha, beta);
|
||
return num - den;
|
||
}
|
||
|
||
/// <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 BetaPrimeDistribution(this.alpha, this.beta);
|
||
}
|
||
|
||
/// <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, "BetaPrime(x; α = {0}, β = {1})",
|
||
alpha.ToString(format, formatProvider),
|
||
beta.ToString(format, formatProvider));
|
||
}
|
||
|
||
}
|
||
}
|