R1NonCentralCumulantInvariant.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>R1NonCentralCumulantInvariant</i> implements the Cumulant Invariant Transformation 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 R1NonCentralCumulantInvariant
  117.     extends org.drip.measure.chisquare.R1NonCentral
  118. {
  119.     private double _sankaranB = java.lang.Double.NaN;

  121.     private double transform (
  122.         final double x)
  123.     {
  124.         org.drip.measure.chisquare.R1NonCentralParameters r1NonCentralParameters = parameters();

  126.         return java.lang.Math.sqrt (
  127.             (
  128.                 x - _sankaranB
  129.             ) / (
  130.                 r1NonCentralParameters.degreesOfFreedom() + r1NonCentralParameters.nonCentralityParameter()
  131.             )
  132.         );
  133.     }

  135.     private double inverseTransform (
  136.         final double y)
  137.     {
  138.         org.drip.measure.chisquare.R1NonCentralParameters r1NonCentralParameters = parameters();

  140.         return y * y * (
  141.             r1NonCentralParameters.degreesOfFreedom() + r1NonCentralParameters.nonCentralityParameter()
  142.         ) + _sankaranB;
  143.     }

  145.     /**
  146.      * Construct the Second Cumulant Invariant Instance of R1NonCentralCumulantInvariant
  147.      * 
  148.      * @param degreesOfFreedom Degrees of Freedom
  149.      * @param nonCentralityParameter Non-centrality Parameter
  150.      * @param gammaEstimator Gamma Estimator
  151.      * @param digammaEstimator Digamma Estimator
  152.      * @param lowerIncompleteGammaEstimator Lower Incomplete Gamma Estimator
  153.      * @param modifiedBesselFirstKindEstimator Modified Bessel First Kind Estimator
  154.      * 
  155.      * @return The Second Cumulant Invariant Instance of R1NonCentralCumulantInvariant
  156.      */

  158.     public static final R1NonCentralCumulantInvariant InvariantSecondCumulant (
  159.         final int degreesOfFreedom,
  160.         final double nonCentralityParameter,
  161.         final org.drip.function.definition.R1ToR1 gammaEstimator,
  162.         final org.drip.function.definition.R1ToR1 digammaEstimator,
  163.         final org.drip.function.definition.R2ToR1 lowerIncompleteGammaEstimator,
  164.         final org.drip.specialfunction.definition.ModifiedBesselFirstKindEstimator
  165.             modifiedBesselFirstKindEstimator)
  166.     {
  167.         try
  168.         {
  169.             return new R1NonCentralCumulantInvariant (
  170.                 new org.drip.measure.chisquare.R1NonCentralParameters (
  171.                     degreesOfFreedom,
  172.                     nonCentralityParameter
  173.                 ),
  174.                 gammaEstimator,
  175.                 digammaEstimator,
  176.                 lowerIncompleteGammaEstimator,
  177.                 modifiedBesselFirstKindEstimator,
  178.                 (degreesOfFreedom - 1.) / 2.
  179.             );
  180.         }
  181.         catch (java.lang.Exception e)
  182.         {
  183.             e.printStackTrace();
  184.         }

  186.         return null;
  187.     }

  189.     /**
  190.      * Construct the Third Cumulant Invariant Instance of R1NonCentralCumulantInvariant
  191.      * 
  192.      * @param degreesOfFreedom Degrees of Freedom
  193.      * @param nonCentralityParameter Non-centrality Parameter
  194.      * @param gammaEstimator Gamma Estimator
  195.      * @param digammaEstimator Digamma Estimator
  196.      * @param lowerIncompleteGammaEstimator Lower Incomplete Gamma Estimator
  197.      * @param modifiedBesselFirstKindEstimator Modified Bessel First Kind Estimator
  198.      * 
  199.      * @return The Third Cumulant Invariant Instance of R1NonCentralCumulantInvariant
  200.      */

  202.     public static final R1NonCentralCumulantInvariant InvariantThirdCumulant (
  203.         final int degreesOfFreedom,
  204.         final double nonCentralityParameter,
  205.         final org.drip.function.definition.R1ToR1 gammaEstimator,
  206.         final org.drip.function.definition.R1ToR1 digammaEstimator,
  207.         final org.drip.function.definition.R2ToR1 lowerIncompleteGammaEstimator,
  208.         final org.drip.specialfunction.definition.ModifiedBesselFirstKindEstimator
  209.             modifiedBesselFirstKindEstimator)
  210.     {
  211.         try
  212.         {
  213.             return new R1NonCentralCumulantInvariant (
  214.                 new org.drip.measure.chisquare.R1NonCentralParameters (
  215.                     degreesOfFreedom,
  216.                     nonCentralityParameter
  217.                 ),
  218.                 gammaEstimator,
  219.                 digammaEstimator,
  220.                 lowerIncompleteGammaEstimator,
  221.                 modifiedBesselFirstKindEstimator,
  222.                 (degreesOfFreedom - 1.) / 3.
  223.             );
  224.         }
  225.         catch (java.lang.Exception e)
  226.         {
  227.             e.printStackTrace();
  228.         }

  230.         return null;
  231.     }

  233.     /**
  234.      * Construct the Fourth Cumulant Invariant Instance of R1NonCentralCumulantInvariant
  235.      * 
  236.      * @param degreesOfFreedom Degrees of Freedom
  237.      * @param nonCentralityParameter Non-centrality Parameter
  238.      * @param gammaEstimator Gamma Estimator
  239.      * @param digammaEstimator Digamma Estimator
  240.      * @param lowerIncompleteGammaEstimator Lower Incomplete Gamma Estimator
  241.      * @param modifiedBesselFirstKindEstimator Modified Bessel First Kind Estimator
  242.      * 
  243.      * @return The Fourth Cumulant Invariant Instance of R1NonCentralCumulantInvariant
  244.      */

  246.     public static final R1NonCentralCumulantInvariant InvariantFourthCumulant (
  247.         final int degreesOfFreedom,
  248.         final double nonCentralityParameter,
  249.         final org.drip.function.definition.R1ToR1 gammaEstimator,
  250.         final org.drip.function.definition.R1ToR1 digammaEstimator,
  251.         final org.drip.function.definition.R2ToR1 lowerIncompleteGammaEstimator,
  252.         final org.drip.specialfunction.definition.ModifiedBesselFirstKindEstimator
  253.             modifiedBesselFirstKindEstimator)
  254.     {
  255.         try
  256.         {
  257.             return new R1NonCentralCumulantInvariant (
  258.                 new org.drip.measure.chisquare.R1NonCentralParameters (
  259.                     degreesOfFreedom,
  260.                     nonCentralityParameter
  261.                 ),
  262.                 gammaEstimator,
  263.                 digammaEstimator,
  264.                 lowerIncompleteGammaEstimator,
  265.                 modifiedBesselFirstKindEstimator,
  266.                 (degreesOfFreedom - 1.) / 4.
  267.             );
  268.         }
  269.         catch (java.lang.Exception e)
  270.         {
  271.             e.printStackTrace();
  272.         }

  274.         return null;
  275.     }

  277.     /**
  278.      * R1NonCentralCumulantInvariant Constructor
  279.      * 
  280.      * @param r1NonCentralParameters R<sup>1</sup> Non-central Parameters
  281.      * @param gammaEstimator Gamma Estimator
  282.      * @param digammaEstimator Digamma Estimator
  283.      * @param lowerIncompleteGammaEstimator Lower Incomplete Gamma Estimator
  284.      * @param modifiedBesselFirstKindEstimator Modified Bessel First Kind Estimator
  285.      * @param sankaranB Sankaran (1963) "B"
  286.      * 
  287.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  288.      */

  290.     public R1NonCentralCumulantInvariant (
  291.         final org.drip.measure.chisquare.R1NonCentralParameters r1NonCentralParameters,
  292.         final org.drip.function.definition.R1ToR1 gammaEstimator,
  293.         final org.drip.function.definition.R1ToR1 digammaEstimator,
  294.         final org.drip.function.definition.R2ToR1 lowerIncompleteGammaEstimator,
  295.         final org.drip.specialfunction.definition.ModifiedBesselFirstKindEstimator
  296.             modifiedBesselFirstKindEstimator,
  297.         final double sankaranB)
  298.         throws java.lang.Exception
  299.     {
  300.         super (
  301.             r1NonCentralParameters,
  302.             gammaEstimator,
  303.             digammaEstimator,
  304.             lowerIncompleteGammaEstimator,
  305.             modifiedBesselFirstKindEstimator
  306.         );

  308.         if (!org.drip.numerical.common.NumberUtil.IsValid (
  309.             _sankaranB = sankaranB
  310.         ))
  311.         {
  312.             throw new java.lang.Exception (
  313.                 "R1NonCentralCumulantInvariant Constructor => Invalid Inputs"
  314.             );
  315.         }
  316.     }

  318.     /**
  319.      * Retrieve the Sankaran (1963) "B"
  320.      * 
  321.      * @return Sankaran (1963) "B"
  322.      */

  324.     public double sankaranB()
  325.     {
  326.         return _sankaranB;
  327.     }

  329.     @Override public double density (
  330.         final double x)
  331.         throws java.lang.Exception
  332.     {
  333.         return super.density (
  334.             transform (
  335.                 x
  336.             )
  337.         );
  338.     }

  340.     @Override public double cumulative (
  341.         final double x)
  342.         throws java.lang.Exception
  343.     {
  344.         return super.cumulative (
  345.             transform (
  346.                 x
  347.             )
  348.         );
  349.     }

  351.     @Override public double invCumulative (
  352.         final double y)
  353.         throws java.lang.Exception
  354.     {
  355.         return inverseTransform (
  356.             super.invCumulative (
  357.                 y
  358.             )
  359.         );
  360.     }
  361. }
Created with JaCoCo 0.7.9.201702052155