R1NonCentralComposite.java

  1. package org.drip.measure.chisquare;

  3. /*
  4.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  5.  */

  7. /*!
  8.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  9.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  10.  * 
  11.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  12.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  13.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  14.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  15.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  16.  *      and computational support.
  17.  *  
  18.  *      https://lakshmidrip.github.io/DROP/
  19.  *  
  20.  *  DROP is composed of three modules:
  21.  *  
  22.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  23.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  24.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  25.  * 
  26.  *  DROP Product Core implements libraries for the following:
  27.  *  - Fixed Income Analytics
  28.  *  - Loan Analytics
  29.  *  - Transaction Cost Analytics
  30.  * 
  31.  *  DROP Portfolio Core implements libraries for the following:
  32.  *  - Asset Allocation Analytics
  33.  *  - Asset Liability Management Analytics
  34.  *  - Capital Estimation Analytics
  35.  *  - Exposure Analytics
  36.  *  - Margin Analytics
  37.  *  - XVA Analytics
  38.  * 
  39.  *  DROP Computational Core implements libraries for the following:
  40.  *  - Algorithm Support
  41.  *  - Computation Support
  42.  *  - Function Analysis
  43.  *  - Model Validation
  44.  *  - Numerical Analysis
  45.  *  - Numerical Optimizer
  46.  *  - Spline Builder
  47.  *  - Statistical Learning
  48.  * 
  49.  *  Documentation for DROP is Spread Over:
  50.  * 
  51.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  52.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  53.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  54.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  55.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  56.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  57.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  58.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  59.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  60.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  61.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  62.  * 
  63.  *  Licensed under the Apache License, Version 2.0 (the "License");
  64.  *      you may not use this file except in compliance with the License.
  65.  *   
  66.  *  You may obtain a copy of the License at
  67.  *      http://www.apache.org/licenses/LICENSE-2.0
  68.  *  
  69.  *  Unless required by applicable law or agreed to in writing, software
  70.  *      distributed under the License is distributed on an "AS IS" BASIS,
  71.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  72.  *  
  73.  *  See the License for the specific language governing permissions and
  74.  *      limitations under the License.
  75.  */

  77. /**
  78.  * <i>R1NonCentralComposite</i> implements Composite R<sup>1</sup> Non-central Chi-Square Distributions. The
  79.  *  References are:
  80.  * 
  81.  * <br><br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Johnson, N. L., S. Kotz, and N. Balakrishnan (1995): <i>Continuous Univariate Distributions
  85.  *              2<sup>nd</sup> Edition</i> <b>John Wiley and Sons</b>
  86.  *      </li>
  87.  *      <li>
  88.  *          Muirhead, R. (2005): <i>Aspects of Multivariate Statistical Theory 2<sup>nd</sup> Edition</i>
  89.  *              <b>Wiley</b>
  90.  *      </li>
  91.  *      <li>
  92.  *          Non-central Chi-Squared Distribution (2019): Chi-Squared Function
  93.  *              https://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution
  94.  *      </li>
  95.  *      <li>
  96.  *          Sankaran, M. (1963): Approximations to the Non-Central Chi-Square Distribution <i>Biometrika</i>
  97.  *              <b>50 (1-2)</b> 199-204
  98.  *      </li>
  99.  *      <li>
  100.  *          Young, D. S. (2010): tolerance: An R Package for Estimating Tolerance Intervals <i>Journal of
  101.  *              Statistical Software</i> <b>36 (5)</b> 1-39
  102.  *      </li>
  103.  *  </ul>
  104.  *
  105.  *  <br><br>
  106.  *  <ul>
  107.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  108.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  109.  *      <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>
  110.  *      <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>
  111.  *  </ul>
  112.  *
  113.  * @author Lakshmi Krishnamurthy
  114.  */

  116. public class R1NonCentralComposite
  117. {

  119.     /**
  120.      * Generate a Random Variable following the Rice Distribution
  121.      * 
  122.      * @param lambda Lambda of the Rice Distribution
  123.      * 
  124.      * @return Random Variable following the Rice Distribution
  125.      * 
  126.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  127.      */

  129.     public static final double RandomRice (
  130.         final double lambda)
  131.         throws java.lang.Exception
  132.     {
  133.         if (!org.drip.numerical.common.NumberUtil.IsValid (
  134.                 lambda
  135.             ) || 0. >= lambda
  136.         )
  137.         {
  138.             throw new java.lang.Exception (
  139.                 "R1NonCentralComposite::RandomRice => Invalid Inputs"
  140.             );
  141.         }

  143.         double random1 = new org.drip.measure.gaussian.R1UnivariateNormal (
  144.             0.,
  145.             1.
  146.         ).random();

  148.         double random2 = new org.drip.measure.gaussian.R1UnivariateNormal (
  149.             java.lang.Math.sqrt (
  150.                 lambda
  151.             ),
  152.             1.
  153.         ).random();

  155.         return random1 * random1 + random2 * random2;
  156.     }

  158.     /**
  159.      * Generate a Non-Central F Distribution Based off of R<sup>1</sup> Non-central Chi-Square Distribution
  160.      *  Pair
  161.      * 
  162.      * @param r1NonCentral1 R<sup>1</sup> Non-central Chi-Square Distribution #1
  163.      * @param r1NonCentral2 R<sup>1</sup> Non-central Chi-Square Distribution #2
  164.      * 
  165.      * @return Non-Central F Distribution Random Variable
  166.      * 
  167.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  168.      */

  170.     public static final double RandomNonCentralF (
  171.         final org.drip.measure.chisquare.R1NonCentral r1NonCentral1,
  172.         final org.drip.measure.chisquare.R1NonCentral r1NonCentral2)
  173.         throws java.lang.Exception
  174.     {
  175.         if (null == r1NonCentral1 ||
  176.             null == r1NonCentral2)
  177.         {
  178.             throw new java.lang.Exception (
  179.                 "R1NonCentralComposite::RandomNonCentralF => Invalid Inputs"
  180.             );
  181.         }

  183.         return r1NonCentral1.random() * r1NonCentral2.parameters().degreesOfFreedom() /
  184.             r1NonCentral1.parameters().degreesOfFreedom() / r1NonCentral2.random();
  185.     }

  187.     /**
  188.      * Generate the R<sup>1</sup> Non-central Distribution corresponding to the Sum of Independent
  189.      *      R<sup>1</sup> Non-central Distributions
  190.      * 
  191.      * @param r1NonCentralArray Array of Independent R<sup>1</sup> Non-central Distributions
  192.      * 
  193.      * @return R<sup>1</sup> Non-central Distribution corresponding to the Sum of Independent R<sup>1</sup>
  194.      *      Non-central Distributions
  195.      */

  197.     public static final org.drip.measure.chisquare.R1NonCentral IndependentSum (
  198.         final org.drip.measure.chisquare.R1NonCentral[] r1NonCentralArray)
  199.     {
  200.         if (null == r1NonCentralArray)
  201.         {
  202.             return null;
  203.         }

  205.         double compositeDegreesOfFreedom = 0.;
  206.         double compositeNonCentralityParameter = 0.;
  207.         int nonCentralDistributionCount = r1NonCentralArray.length;

  209.         for (int nonCentralDistributionIndex = 0;
  210.             nonCentralDistributionIndex < nonCentralDistributionCount;
  211.             ++nonCentralDistributionIndex
  212.             )
  213.         {
  214.             if (null == r1NonCentralArray[nonCentralDistributionIndex])
  215.             {
  216.                 return null;
  217.             }

  219.             org.drip.measure.chisquare.R1NonCentralParameters r1NonCentralParameters =
  220.                 r1NonCentralArray[nonCentralDistributionIndex].parameters();

  222.             compositeDegreesOfFreedom = r1NonCentralParameters.degreesOfFreedom();

  224.             compositeNonCentralityParameter = r1NonCentralParameters.nonCentralityParameter();
  225.         }

  227.         return org.drip.measure.chisquare.R1NonCentral.Standard (
  228.             compositeDegreesOfFreedom,
  229.             compositeNonCentralityParameter,
  230.             r1NonCentralArray[0].gammaEstimator(),
  231.             r1NonCentralArray[0].digammaEstimator(),
  232.             r1NonCentralArray[0].lowerIncompleteGammaEstimator(),
  233.             r1NonCentralArray[0].modifiedBesselFirstKindEstimator()
  234.         );
  235.     }
  236. }
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