NonCentralCumulantMoments.java

  1. package org.drip.sample.chisquaredistribution;

  3. import org.drip.function.definition.R1ToR1;
  4. import org.drip.function.definition.R2ToR1;
  5. import org.drip.measure.chisquare.R1NonCentral;
  6. import org.drip.numerical.common.FormatUtil;
  7. import org.drip.service.env.EnvManager;
  8. import org.drip.specialfunction.bessel.ModifiedFirstFrobeniusSeriesEstimator;
  9. import org.drip.specialfunction.definition.ModifiedBesselFirstKindEstimator;
  10. import org.drip.specialfunction.digamma.CumulativeSeriesEstimator;
  11. import org.drip.specialfunction.gamma.EulerIntegralSecondKind;
  12. import org.drip.specialfunction.incompletegamma.LowerEulerIntegral;

  14. /*
  15.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  16.  */

  18. /*!
  19.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  20.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  21.  * 
  22.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  23.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  24.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  25.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  26.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  27.  *      and computational support.
  28.  *  
  29.  *      https://lakshmidrip.github.io/DROP/
  30.  *  
  31.  *  DROP is composed of three modules:
  32.  *  
  33.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  34.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  35.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  36.  * 
  37.  *  DROP Product Core implements libraries for the following:
  38.  *  - Fixed Income Analytics
  39.  *  - Loan Analytics
  40.  *  - Transaction Cost Analytics
  41.  * 
  42.  *  DROP Portfolio Core implements libraries for the following:
  43.  *  - Asset Allocation Analytics
  44.  *  - Asset Liability Management Analytics
  45.  *  - Capital Estimation Analytics
  46.  *  - Exposure Analytics
  47.  *  - Margin Analytics
  48.  *  - XVA Analytics
  49.  * 
  50.  *  DROP Computational Core implements libraries for the following:
  51.  *  - Algorithm Support
  52.  *  - Computation Support
  53.  *  - Function Analysis
  54.  *  - Model Validation
  55.  *  - Numerical Analysis
  56.  *  - Numerical Optimizer
  57.  *  - Spline Builder
  58.  *  - Statistical Learning
  59.  * 
  60.  *  Documentation for DROP is Spread Over:
  61.  * 
  62.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  63.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  64.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  65.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  66.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  67.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  68.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  69.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  70.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  71.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  72.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  73.  * 
  74.  *  Licensed under the Apache License, Version 2.0 (the "License");
  75.  *      you may not use this file except in compliance with the License.
  76.  *   
  77.  *  You may obtain a copy of the License at
  78.  *      http://www.apache.org/licenses/LICENSE-2.0
  79.  *  
  80.  *  Unless required by applicable law or agreed to in writing, software
  81.  *      distributed under the License is distributed on an "AS IS" BASIS,
  82.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  83.  *  
  84.  *  See the License for the specific language governing permissions and
  85.  *      limitations under the License.
  86.  */

  88. /**
  89.  * <i>NonCentralCumulantMoments</i> illustrates the Computation of the Leading Cumulants and the Non-Central
  90.  *  Moments. The References are:
  91.  * 
  92.  * <br><br>
  93.  *  <ul>
  94.  *      <li>
  95.  *          Johnson, N. L., S. Kotz, and N. Balakrishnan (1995): <i>Continuous Univariate Distributions
  96.  *              2<sup>nd</sup> Edition</i> <b>John Wiley and Sons</b>
  97.  *      </li>
  98.  *      <li>
  99.  *          Muirhead, R. (2005): <i>Aspects of Multivariate Statistical Theory 2<sup>nd</sup> Edition</i>
  100.  *              <b>Wiley</b>
  101.  *      </li>
  102.  *      <li>
  103.  *          Non-central Chi-Squared Distribution (2019): Chi-Squared Function
  104.  *              https://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution
  105.  *      </li>
  106.  *      <li>
  107.  *          Sankaran, M. (1963): Approximations to the Non-Central Chi-Square Distribution <i>Biometrika</i>
  108.  *              <b>50 (1-2)</b> 199-204
  109.  *      </li>
  110.  *      <li>
  111.  *          Young, D. S. (2010): tolerance: An R Package for Estimating Tolerance Intervals <i>Journal of
  112.  *              Statistical Software</i> <b>36 (5)</b> 1-39
  113.  *      </li>
  114.  *  </ul>
  115.  *
  116.  *  <br><br>
  117.  *  <ul>
  118.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  119.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  120.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">DROP API Construction and Usage</a></li>
  121.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/chisquaredistribution/README.md">Chi-Square Distribution Usage/Properties</a></li>
  122.  *  </ul>
  123.  *
  124.  * @author Lakshmi Krishnamurthy
  125.  */

  127. public class NonCentralCumulantMoments
  128. {

  130.     private static final R2ToR1 LowerIncompleteGamma()
  131.         throws Exception
  132.     {
  133.         return new R2ToR1()
  134.         {
  135.             @Override public double evaluate (
  136.                 final double s,
  137.                 final double t)
  138.                 throws Exception
  139.             {
  140.                 return new LowerEulerIntegral (
  141.                     null,
  142.                     t
  143.                 ).evaluate (
  144.                     s
  145.                 );
  146.             }
  147.         };
  148.     }

  150.     public static final void main (
  151.         final String[] argumentArray)
  152.         throws Exception
  153.     {
  154.         EnvManager.InitEnv (
  155.             ""
  156.         );

  158.         int digammaTermCount = 1000;
  159.         int besselFirstTermCount = 20;
  160.         double[] nonCentralityParameterArray =
  161.         {
  162.             0.5,
  163.             1.0,
  164.             1.5,
  165.             2.0,
  166.             2.5,
  167.             3.0,
  168.             3.5,
  169.             4.0,
  170.         };
  171.         int[] dofArray =
  172.         {
  173.              2,
  174.              3,
  175.              4,
  176.              5,
  177.              6,
  178.              7,
  179.              8,
  180.              9,
  181.         };
  182.         int[] nArray =
  183.         {
  184.             1,
  185.             2,
  186.             3,
  187.             4,
  188.             5,
  189.             6,
  190.         };

  192.         R1ToR1 gammaEstimator = new EulerIntegralSecondKind (
  193.             null
  194.         );

  196.         R2ToR1 lowerIncompleteGammaEstimator = LowerIncompleteGamma();

  198.         R1ToR1 digammaEstimator = CumulativeSeriesEstimator.AbramowitzStegun2007 (
  199.             digammaTermCount
  200.         );

  202.         ModifiedBesselFirstKindEstimator modifiedBesselFirstKindEstimator =
  203.             ModifiedFirstFrobeniusSeriesEstimator.Standard (
  204.                 gammaEstimator,
  205.                 besselFirstTermCount
  206.             );

  208.         System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------||");

  210.         System.out.println ("\t|                                   NON CENTRAL CHI-SQUARE CUMULANTS AND NON-CENTRAL MOMENTS                                   ||");

  212.         System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------||");

  214.         System.out.println ("\t|        L -> R:                                                                                                               ||");

  216.         System.out.println ("\t|                - Degrees of Freedom; Non Centrality Parameter                                                                ||");

  218.         System.out.println ("\t|                - Cumulant                                                                                                    ||");

  220.         System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------||");

  222.         for (double nonCentralityParameter : nonCentralityParameterArray)
  223.         {
  224.             for (int dof : dofArray)
  225.             {
  226.                 R1NonCentral r1UnivariateNonCentral = R1NonCentral.Standard (
  227.                     dof,
  228.                     nonCentralityParameter,
  229.                     gammaEstimator,
  230.                     digammaEstimator,
  231.                     lowerIncompleteGammaEstimator,
  232.                     modifiedBesselFirstKindEstimator
  233.                 );

  235.                 String display = "\t| [" +
  236.                     FormatUtil.FormatDouble (dof, 2, 0, 1., false) + " | " +
  237.                     FormatUtil.FormatDouble (nonCentralityParameter, 1, 1, 1., false) +
  238.                 "] =>";

  240.                 for (int n : nArray)
  241.                 {
  242.                     display = display + " " + FormatUtil.FormatDouble (
  243.                         r1UnivariateNonCentral.cumulant (
  244.                             n
  245.                         ), 6, 0, 1., false
  246.                     ) + " |";
  247.                 }

  249.                 System.out.println (display + "|");
  250.             }

  252.             System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------||");
  253.         }

  255.         System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------||");

  257.         System.out.println();

  259.         System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------||");

  261.         System.out.println ("\t|                                   NON CENTRAL CHI-SQUARE CUMULANTS AND NON-CENTRAL MOMENTS                                   ||");

  263.         System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------||");

  265.         System.out.println ("\t|        L -> R:                                                                                                               ||");

  267.         System.out.println ("\t|                - Degrees of Freedom; Non Centrality Parameter                                                                ||");

  269.         System.out.println ("\t|                - Non-central Moment                                                                                          ||");

  271.         System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------||");

  273.         for (double nonCentralityParameter : nonCentralityParameterArray)
  274.         {
  275.             for (int dof : dofArray)
  276.             {
  277.                 R1NonCentral r1UnivariateNonCentral = R1NonCentral.Standard (
  278.                     dof,
  279.                     nonCentralityParameter,
  280.                     gammaEstimator,
  281.                     digammaEstimator,
  282.                     lowerIncompleteGammaEstimator,
  283.                     modifiedBesselFirstKindEstimator
  284.                 );

  286.                 String display = "\t| [" +
  287.                     FormatUtil.FormatDouble (dof, 2, 0, 1., false) + " | " +
  288.                     FormatUtil.FormatDouble (nonCentralityParameter, 1, 1, 1., false) +
  289.                 "] =>";

  291.                 for (int n : nArray)
  292.                 {
  293.                     display = display + " " + FormatUtil.FormatDouble (
  294.                         r1UnivariateNonCentral.nonCentralMoment (
  295.                             n
  296.                         ), 8, 0, 1., false
  297.                     ) + " |";
  298.                 }

  300.                 System.out.println (display + "|");
  301.             }

  303.             System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------||");
  304.         }

  306.         System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------||");

  308.         System.out.println();

  310.         EnvManager.TerminateEnv();
  311.     }
  312. }
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