R1ShapeScaleComposite.java

  1. package org.drip.measure.gamma;

  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>R1ShapeScaleComposite</i> implements the Scale-Scale Composite Measures. The References are:
  79.  * 
  80.  * <br><br>
  81.  *  <ul>
  82.  *      <li>
  83.  *          Devroye, L. (1986): <i>Non-Uniform Random Variate Generation</i> <b>Springer-Verlag</b> New York
  84.  *      </li>
  85.  *      <li>
  86.  *          Gamma Distribution (2019): Gamma Distribution
  87.  *              https://en.wikipedia.org/wiki/Chi-squared_distribution
  88.  *      </li>
  89.  *      <li>
  90.  *          Louzada, F., P. L. Ramos, and E. Ramos (2019): A Note on Bias of Closed-Form Estimators for the
  91.  *              Gamma Distribution Derived From Likelihood Equations <i>The American Statistician</i> <b>73
  92.  *              (2)</b> 195-199
  93.  *      </li>
  94.  *      <li>
  95.  *          Minka, T. (2002): Estimating a Gamma distribution https://tminka.github.io/papers/minka-gamma.pdf
  96.  *      </li>
  97.  *      <li>
  98.  *          Ye, Z. S., and N. Chen (2017): Closed-Form Estimators for the Gamma Distribution Derived from
  99.  *              Likelihood Equations <i>The American Statistician</i> <b>71 (2)</b> 177-181
  100.  *      </li>
  101.  *  </ul>
  102.  *
  103.  *  <br><br>
  104.  *  <ul>
  105.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  106.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  107.  *      <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>
  108.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/gamma/README.md">R<sup>1</sup> Gamma Distribution Implementation/Properties</a></li>
  109.  *  </ul>
  110.  *
  111.  * @author Lakshmi Krishnamurthy
  112.  */

  114. public class R1ShapeScaleComposite
  115. {

  117.     /**
  118.      * Generate a Random Number that follows the F Distribution
  119.      * 
  120.      * @param gammaDistribution1 Gamma Distribution #1
  121.      * @param gammaDistribution2 Gamma Distribution #2
  122.      * 
  123.      * @return Random Number that follows the F Distribution
  124.      * 
  125.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  126.      */

  128.     public static final double RandomF (
  129.         final org.drip.measure.gamma.R1ShapeScaleDiscrete gammaDistribution1,
  130.         final org.drip.measure.gamma.R1ShapeScaleDiscrete gammaDistribution2)
  131.         throws java.lang.Exception
  132.     {
  133.         if (null == gammaDistribution1 ||
  134.             null == gammaDistribution2)
  135.         {
  136.             throw new java.lang.Exception (
  137.                 "R1ShapeScaleComposite::RandomF => Invalid Inputs"
  138.             );
  139.         }

  141.         org.drip.measure.gamma.ShapeScaleParameters shapeScaleParameters1 =
  142.             gammaDistribution1.shapeScaleParameters();

  144.         org.drip.measure.gamma.ShapeScaleParameters shapeScaleParameters2 =
  145.             gammaDistribution2.shapeScaleParameters();

  147.         return gammaDistribution1.random() / (
  148.             shapeScaleParameters1.shape() * shapeScaleParameters1.scale()
  149.         ) / (gammaDistribution2.random() / (
  150.             shapeScaleParameters2.shape() * shapeScaleParameters2.scale()
  151.         ));
  152.     }

  154.     /**
  155.      * Generate a Random Number that follows the Beta Prime Distribution
  156.      * 
  157.      * @param gammaDistribution1 Gamma Distribution #1
  158.      * @param gammaDistribution2 Gamma Distribution #2
  159.      * 
  160.      * @return Random Number that follows the Beta Prime Distribution
  161.      * 
  162.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  163.      */

  165.     public static final double RandomBetaPrime (
  166.         final org.drip.measure.gamma.R1ShapeScaleDiscrete gammaDistribution1,
  167.         final org.drip.measure.gamma.R1ShapeScaleDiscrete gammaDistribution2)
  168.         throws java.lang.Exception
  169.     {
  170.         if (null == gammaDistribution1 ||
  171.             null == gammaDistribution2)
  172.         {
  173.             throw new java.lang.Exception (
  174.                 "R1ShapeScaleComposite::RandomBetaPrime => Invalid Inputs"
  175.             );
  176.         }

  178.         return gammaDistribution1.random() / gammaDistribution2.random();
  179.     }

  181.     /**
  182.      * Generate a Random Number that follows the Beta Distribution
  183.      * 
  184.      * @param gammaDistribution1 Gamma Distribution #1
  185.      * @param gammaDistribution2 Gamma Distribution #2
  186.      * 
  187.      * @return Random Number that follows the Beta Distribution
  188.      * 
  189.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  190.      */

  192.     public static final double RandomBeta (
  193.         final org.drip.measure.gamma.R1ShapeScaleDiscrete gammaDistribution1,
  194.         final org.drip.measure.gamma.R1ShapeScaleDiscrete gammaDistribution2)
  195.         throws java.lang.Exception
  196.     {
  197.         if (null == gammaDistribution1 ||
  198.             null == gammaDistribution2)
  199.         {
  200.             throw new java.lang.Exception (
  201.                 "R1ShapeScaleComposite::RandomBeta => Invalid Inputs"
  202.             );
  203.         }

  205.         double scale = gammaDistribution1.shapeScaleParameters().scale();

  207.         if (scale != gammaDistribution2.shapeScaleParameters().scale())
  208.         {
  209.             throw new java.lang.Exception (
  210.                 "R1ShapeScaleComposite::RandomBeta => Invalid Inputs"
  211.             );
  212.         }

  214.         double gammaDistribution1Random = gammaDistribution1.random();

  216.         return gammaDistribution1Random / (gammaDistribution1Random + gammaDistribution2.random());
  217.     }

  219.     /**
  220.      * Generate a Random Vector that follows the Dirichlet Distribution
  221.      * 
  222.      * @param gammaDistributionArray Gamma Distribution Array
  223.      * 
  224.      * @return Random Vector that follows the Dirichlet Distribution
  225.      */

  227.     public static final double[] RandomDirichletVector (
  228.         final org.drip.measure.gamma.R1ShapeScaleDiscrete[] gammaDistributionArray)
  229.     {
  230.         if (null == gammaDistributionArray)
  231.         {
  232.             return null;
  233.         }

  235.         double dirichletSum = 0.;
  236.         int dirichletVectorCount = gammaDistributionArray.length;
  237.         double[] randomDirichletVector = new double[dirichletVectorCount];

  239.         if (0 == dirichletVectorCount)
  240.         {
  241.             return null;
  242.         }

  244.         for (int dirichletVectorIndex = 0;
  245.             dirichletVectorIndex < dirichletVectorCount;
  246.             ++dirichletVectorIndex)
  247.         {
  248.             if (null == gammaDistributionArray[dirichletVectorIndex] ||
  249.                 1 != gammaDistributionArray[dirichletVectorIndex].shapeScaleParameters().scale())
  250.             {
  251.                 return null;
  252.             }

  254.             try
  255.             {
  256.                 dirichletSum = dirichletSum + (
  257.                     randomDirichletVector[dirichletVectorIndex] =
  258.                     gammaDistributionArray[dirichletVectorIndex].random()
  259.                 );
  260.             }
  261.             catch (java.lang.Exception e)
  262.             {
  263.                 e.printStackTrace();

  265.                 return null;
  266.             }
  267.         }

  269.         for (int dirichletVectorIndex = 0;
  270.             dirichletVectorIndex < dirichletVectorCount;
  271.             ++dirichletVectorIndex)
  272.         {
  273.             randomDirichletVector[dirichletVectorIndex] = randomDirichletVector[dirichletVectorIndex] /
  274.                 dirichletSum;
  275.         }

  277.         return randomDirichletVector;
  278.     }

  280.     /**
  281.      * Compute the Kullback-Liebler Divergence for the Gamma Distribution Pair
  282.      * 
  283.      * @param gammaDistribution1 Gamma Distribution #1
  284.      * @param gammaDistribution2 Gamma Distribution #2
  285.      * 
  286.      * @return The Kullback-Liebler Divergence for the Gamma Distribution Pair
  287.      * 
  288.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  289.      */

  291.     public static final double KullbackLieblerDivergence (
  292.         final org.drip.measure.gamma.R1ShapeScaleDistribution gammaDistribution1,
  293.         final org.drip.measure.gamma.R1ShapeScaleDistribution gammaDistribution2)
  294.         throws java.lang.Exception
  295.     {
  296.         if (null == gammaDistribution1 ||
  297.             null == gammaDistribution2)
  298.         {
  299.             throw new java.lang.Exception (
  300.                 "R1ShapeScaleComposite::KullbackLieblerDivergence => Invalid Inputs"
  301.             );
  302.         }

  304.         org.drip.measure.gamma.ShapeScaleParameters shapeScaleParameters1 =
  305.             gammaDistribution1.shapeScaleParameters();

  307.         org.drip.measure.gamma.ShapeScaleParameters shapeScaleParameters2 =
  308.             gammaDistribution2.shapeScaleParameters();

  310.         double scale1 = shapeScaleParameters1.scale();

  312.         double scale2 = shapeScaleParameters2.scale();

  314.         double shape1 = shapeScaleParameters1.shape();

  316.         double shape2 = shapeScaleParameters2.shape();

  318.         org.drip.function.definition.R1ToR1 gammaEstimator = gammaDistribution1.gammaEstimator();

  320.         return (shape1 - shape2) * gammaDistribution1.digammaEstimator().evaluate (
  321.             shape1
  322.         ) - gammaEstimator.evaluate (
  323.             shape1
  324.         ) + gammaEstimator.evaluate (
  325.             shape2
  326.         ) + shape2 * (
  327.             java.lang.Math.log (
  328.                 scale2
  329.             ) - java.lang.Math.log (
  330.                 scale1
  331.             )
  332.         ) + shape1 * (scale1 - scale2) / scale1;
  333.     }
  334. }
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