R1NonCentralComposite.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>R1NonCentralComposite</i> implements Composite R<sup>1</sup> Non-central Chi-Square Distributions. 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 R1NonCentralComposite
{
/**
* Generate a Random Variable following the Rice Distribution
*
* @param lambda Lambda of the Rice Distribution
*
* @return Random Variable following the Rice Distribution
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public static final double RandomRice (
final double lambda)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (
lambda
) || 0. >= lambda
)
{
throw new java.lang.Exception (
"R1NonCentralComposite::RandomRice => Invalid Inputs"
);
}
double random1 = new org.drip.measure.gaussian.R1UnivariateNormal (
0.,
1.
).random();
double random2 = new org.drip.measure.gaussian.R1UnivariateNormal (
java.lang.Math.sqrt (
lambda
),
1.
).random();
return random1 * random1 + random2 * random2;
}
/**
* Generate a Non-Central F Distribution Based off of R<sup>1</sup> Non-central Chi-Square Distribution
* Pair
*
* @param r1NonCentral1 R<sup>1</sup> Non-central Chi-Square Distribution #1
* @param r1NonCentral2 R<sup>1</sup> Non-central Chi-Square Distribution #2
*
* @return Non-Central F Distribution Random Variable
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public static final double RandomNonCentralF (
final org.drip.measure.chisquare.R1NonCentral r1NonCentral1,
final org.drip.measure.chisquare.R1NonCentral r1NonCentral2)
throws java.lang.Exception
{
if (null == r1NonCentral1 ||
null == r1NonCentral2)
{
throw new java.lang.Exception (
"R1NonCentralComposite::RandomNonCentralF => Invalid Inputs"
);
}
return r1NonCentral1.random() * r1NonCentral2.parameters().degreesOfFreedom() /
r1NonCentral1.parameters().degreesOfFreedom() / r1NonCentral2.random();
}
/**
* Generate the R<sup>1</sup> Non-central Distribution corresponding to the Sum of Independent
* R<sup>1</sup> Non-central Distributions
*
* @param r1NonCentralArray Array of Independent R<sup>1</sup> Non-central Distributions
*
* @return R<sup>1</sup> Non-central Distribution corresponding to the Sum of Independent R<sup>1</sup>
* Non-central Distributions
*/
public static final org.drip.measure.chisquare.R1NonCentral IndependentSum (
final org.drip.measure.chisquare.R1NonCentral[] r1NonCentralArray)
{
if (null == r1NonCentralArray)
{
return null;
}
double compositeDegreesOfFreedom = 0.;
double compositeNonCentralityParameter = 0.;
int nonCentralDistributionCount = r1NonCentralArray.length;
for (int nonCentralDistributionIndex = 0;
nonCentralDistributionIndex < nonCentralDistributionCount;
++nonCentralDistributionIndex
)
{
if (null == r1NonCentralArray[nonCentralDistributionIndex])
{
return null;
}
org.drip.measure.chisquare.R1NonCentralParameters r1NonCentralParameters =
r1NonCentralArray[nonCentralDistributionIndex].parameters();
compositeDegreesOfFreedom = r1NonCentralParameters.degreesOfFreedom();
compositeNonCentralityParameter = r1NonCentralParameters.nonCentralityParameter();
}
return org.drip.measure.chisquare.R1NonCentral.Standard (
compositeDegreesOfFreedom,
compositeNonCentralityParameter,
r1NonCentralArray[0].gammaEstimator(),
r1NonCentralArray[0].digammaEstimator(),
r1NonCentralArray[0].lowerIncompleteGammaEstimator(),
r1NonCentralArray[0].modifiedBesselFirstKindEstimator()
);
}
}