R1NonCentralAbdelAty.java
package org.drip.measure.chisquare;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
* asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
* analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
* equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
* numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
* and computational support.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
*
* DROP Product Core implements libraries for the following:
* - Fixed Income Analytics
* - Loan Analytics
* - Transaction Cost Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Asset Liability Management Analytics
* - Capital Estimation Analytics
* - Exposure Analytics
* - Margin Analytics
* - XVA Analytics
*
* DROP Computational Core implements libraries for the following:
* - Algorithm Support
* - Computation Support
* - Function Analysis
* - Model Validation
* - Numerical Analysis
* - Numerical Optimizer
* - Spline Builder
* - Statistical Learning
*
* Documentation for DROP is Spread Over:
*
* - Main => https://lakshmidrip.github.io/DROP/
* - Wiki => https://github.com/lakshmiDRIP/DROP/wiki
* - GitHub => https://github.com/lakshmiDRIP/DROP
* - Repo Layout Taxonomy => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
* - Javadoc => https://lakshmidrip.github.io/DROP/Javadoc/index.html
* - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
* - Release Versions => https://lakshmidrip.github.io/DROP/version.html
* - Community Credits => https://lakshmidrip.github.io/DROP/credits.html
* - Issues Catalog => https://github.com/lakshmiDRIP/DROP/issues
* - JUnit => https://lakshmidrip.github.io/DROP/junit/index.html
* - Jacoco => https://lakshmidrip.github.io/DROP/jacoco/index.html
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
*
* You may obtain a copy of the License at
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
*
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/**
* <i>R1NonCentralAbdelAty</i> implements the Abdel-Aty (1954) Wilson-Haferty Approximation for the
* R<sup>1</sup> Non-central Chi-Square Distribution. The References are:
*
* <br><br>
* <ul>
* <li>
* Johnson, N. L., S. Kotz, and N. Balakrishnan (1995): <i>Continuous Univariate Distributions
* 2<sup>nd</sup> Edition</i> <b>John Wiley and Sons</b>
* </li>
* <li>
* Muirhead, R. (2005): <i>Aspects of Multivariate Statistical Theory 2<sup>nd</sup> Edition</i>
* <b>Wiley</b>
* </li>
* <li>
* Non-central Chi-Squared Distribution (2019): Chi-Squared Function
* https://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution
* </li>
* <li>
* Sankaran, M. (1963): Approximations to the Non-Central Chi-Square Distribution <i>Biometrika</i>
* <b>50 (1-2)</b> 199-204
* </li>
* <li>
* Young, D. S. (2010): tolerance: An R Package for Estimating Tolerance Intervals <i>Journal of
* Statistical Software</i> <b>36 (5)</b> 1-39
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/README.md">R<sup>d</sup> Continuous/Discrete Probability Measures</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/chisquare/README.md">Chi-Square Distribution Implementation/Properties</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class R1NonCentralAbdelAty
extends org.drip.measure.chisquare.R1NonCentralWilsonHaferty
{
private double _f = java.lang.Double.NaN;
/**
* Construct a Standard Instance of R1NonCentralAbdelAty
*
* @param degreesOfFreedom Degrees of Freedom
* @param nonCentralityParameter Non-centrality Parameter
*
* @return Standard Instance of R1NonCentralAbdelAty
*/
public static final R1NonCentralAbdelAty Standard (
final int degreesOfFreedom,
final double nonCentralityParameter)
{
if (0 >= degreesOfFreedom ||
!org.drip.numerical.common.NumberUtil.IsValid (
nonCentralityParameter
)
)
{
return null;
}
double f = degreesOfFreedom + nonCentralityParameter * nonCentralityParameter /
(degreesOfFreedom + 2. * nonCentralityParameter);
double twoOver9f = 2. / 9. / f;
try
{
return new R1NonCentralAbdelAty (
new org.drip.measure.chisquare.R1NonCentralParameters (
degreesOfFreedom,
nonCentralityParameter
),
new org.drip.measure.gaussian.R1UnivariateNormal (
1. - twoOver9f,
java.lang.Math.sqrt (
twoOver9f
)
),
f
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
protected R1NonCentralAbdelAty (
final org.drip.measure.chisquare.R1NonCentralParameters r1NonCentralParameters,
final org.drip.measure.gaussian.R1UnivariateNormal r1UnivariateNormal,
final double f)
throws java.lang.Exception
{
super (
r1NonCentralParameters,
r1UnivariateNormal
);
_f = f;
}
/**
* Retrieve the Abdel-Aty (1954) f Parameter
*
* @return The Abdel-Aty (1954) f Parameter
*/
public double f()
{
return _f;
}
@Override public double transform (
final double x)
{
org.drip.measure.chisquare.R1NonCentralParameters parameters = parameters();
return java.lang.Math.pow (
x / (
parameters.degreesOfFreedom() + parameters.nonCentralityParameter()
),
1. / 3.
);
}
@Override public double inverseTransform (
final double wilsonHilferty)
{
org.drip.measure.chisquare.R1NonCentralParameters parameters = parameters();
return wilsonHilferty * wilsonHilferty * wilsonHilferty * (
parameters.degreesOfFreedom() + parameters.nonCentralityParameter()
);
}
}