R1NonCentralAbdelAty.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>R1NonCentralAbdelAty</i> implements the Abdel-Aty (1954) Wilson-Haferty Approximation for the
  79.  *  R<sup>1</sup> Non-central Chi-Square Distribution. The 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 R1NonCentralAbdelAty
  117.     extends org.drip.measure.chisquare.R1NonCentralWilsonHaferty
  118. {
  119.     private double _f = java.lang.Double.NaN;

  121.     /**
  122.      * Construct a Standard Instance of R1NonCentralAbdelAty
  123.      * 
  124.      * @param degreesOfFreedom Degrees of Freedom
  125.      * @param nonCentralityParameter Non-centrality Parameter
  126.      * 
  127.      * @return Standard Instance of R1NonCentralAbdelAty
  128.      */

  130.     public static final R1NonCentralAbdelAty Standard (
  131.         final int degreesOfFreedom,
  132.         final double nonCentralityParameter)
  133.     {
  134.         if (0 >= degreesOfFreedom ||
  135.             !org.drip.numerical.common.NumberUtil.IsValid (
  136.                 nonCentralityParameter
  137.             )
  138.         )
  139.         {
  140.             return null;
  141.         }

  143.         double f = degreesOfFreedom + nonCentralityParameter * nonCentralityParameter /
  144.             (degreesOfFreedom + 2. * nonCentralityParameter);
  145.         double twoOver9f = 2. / 9. / f;

  147.         try
  148.         {
  149.             return new R1NonCentralAbdelAty (
  150.                 new org.drip.measure.chisquare.R1NonCentralParameters (
  151.                     degreesOfFreedom,
  152.                     nonCentralityParameter
  153.                 ),
  154.                 new org.drip.measure.gaussian.R1UnivariateNormal (
  155.                     1. - twoOver9f,
  156.                     java.lang.Math.sqrt (
  157.                         twoOver9f
  158.                     )
  159.                 ),
  160.                 f
  161.             );
  162.         }
  163.         catch (java.lang.Exception e)
  164.         {
  165.             e.printStackTrace();
  166.         }

  168.         return null;
  169.     }

  171.     protected R1NonCentralAbdelAty (
  172.         final org.drip.measure.chisquare.R1NonCentralParameters r1NonCentralParameters,
  173.         final org.drip.measure.gaussian.R1UnivariateNormal r1UnivariateNormal,
  174.         final double f)
  175.         throws java.lang.Exception
  176.     {
  177.         super (
  178.             r1NonCentralParameters,
  179.             r1UnivariateNormal
  180.         );

  182.         _f = f;
  183.     }

  185.     /**
  186.      * Retrieve the Abdel-Aty (1954) f Parameter
  187.      * 
  188.      * @return The Abdel-Aty (1954) f Parameter
  189.      */

  191.     public double f()
  192.     {
  193.         return _f;
  194.     }

  196.     @Override public double transform (
  197.         final double x)
  198.     {
  199.         org.drip.measure.chisquare.R1NonCentralParameters parameters = parameters();

  201.         return java.lang.Math.pow (
  202.             x / (
  203.                 parameters.degreesOfFreedom() + parameters.nonCentralityParameter()
  204.             ),
  205.             1. / 3.
  206.         );
  207.     }

  209.     @Override public double inverseTransform (
  210.         final double wilsonHilferty)
  211.     {
  212.         org.drip.measure.chisquare.R1NonCentralParameters parameters = parameters();

  214.         return wilsonHilferty * wilsonHilferty * wilsonHilferty * (
  215.             parameters.degreesOfFreedom() + parameters.nonCentralityParameter()
  216.         );
  217.     }
  218. }
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