KullbackLieblerDivergence.java

  1. package org.drip.sample.gammadistribution;

  3. import org.drip.function.definition.R1ToR1;
  4. import org.drip.function.definition.R2ToR1;
  5. import org.drip.measure.gamma.R1ShapeScaleComposite;
  6. import org.drip.measure.gamma.R1ShapeScaleDistribution;
  7. import org.drip.numerical.common.FormatUtil;
  8. import org.drip.service.env.EnvManager;
  9. import org.drip.specialfunction.digamma.CumulativeSeriesEstimator;
  10. import org.drip.specialfunction.gamma.EulerIntegralSecondKind;
  11. import org.drip.specialfunction.incompletegamma.LowerEulerIntegral;

  13. /*
  14.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  15.  */

  17. /*!
  18.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  19.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  20.  * 
  21.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  22.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  23.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  24.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  25.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  26.  *      and computational support.
  27.  *  
  28.  *      https://lakshmidrip.github.io/DROP/
  29.  *  
  30.  *  DROP is composed of three modules:
  31.  *  
  32.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  33.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  34.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  35.  * 
  36.  *  DROP Product Core implements libraries for the following:
  37.  *  - Fixed Income Analytics
  38.  *  - Loan Analytics
  39.  *  - Transaction Cost Analytics
  40.  * 
  41.  *  DROP Portfolio Core implements libraries for the following:
  42.  *  - Asset Allocation Analytics
  43.  *  - Asset Liability Management Analytics
  44.  *  - Capital Estimation Analytics
  45.  *  - Exposure Analytics
  46.  *  - Margin Analytics
  47.  *  - XVA Analytics
  48.  * 
  49.  *  DROP Computational Core implements libraries for the following:
  50.  *  - Algorithm Support
  51.  *  - Computation Support
  52.  *  - Function Analysis
  53.  *  - Model Validation
  54.  *  - Numerical Analysis
  55.  *  - Numerical Optimizer
  56.  *  - Spline Builder
  57.  *  - Statistical Learning
  58.  * 
  59.  *  Documentation for DROP is Spread Over:
  60.  * 
  61.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  62.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  63.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  64.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  65.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  66.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  67.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  68.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  69.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  70.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  71.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  72.  * 
  73.  *  Licensed under the Apache License, Version 2.0 (the "License");
  74.  *      you may not use this file except in compliance with the License.
  75.  *   
  76.  *  You may obtain a copy of the License at
  77.  *      http://www.apache.org/licenses/LICENSE-2.0
  78.  *  
  79.  *  Unless required by applicable law or agreed to in writing, software
  80.  *      distributed under the License is distributed on an "AS IS" BASIS,
  81.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  82.  *  
  83.  *  See the License for the specific language governing permissions and
  84.  *      limitations under the License.
  85.  */

  87. /**
  88.  * <i>KullbackLieblerDivergence</i> demonstrates the Kullback-Liebler Divergence between a Pair of
  89.  *  R<sup>1</sup> Gamma Distributions using the Shape/Scale Parameterization. The References are:
  90.  * 
  91.  * <br><br>
  92.  *  <ul>
  93.  *      <li>
  94.  *          Devroye, L. (1986): <i>Non-Uniform Random Variate Generation</i> <b>Springer-Verlag</b> New York
  95.  *      </li>
  96.  *      <li>
  97.  *          Gamma Distribution (2019): Gamma Distribution
  98.  *              https://en.wikipedia.org/wiki/Chi-squared_distribution
  99.  *      </li>
  100.  *      <li>
  101.  *          Louzada, F., P. L. Ramos, and E. Ramos (2019): A Note on Bias of Closed-Form Estimators for the
  102.  *              Gamma Distribution Derived From Likelihood Equations <i>The American Statistician</i> <b>73
  103.  *              (2)</b> 195-199
  104.  *      </li>
  105.  *      <li>
  106.  *          Minka, T. (2002): Estimating a Gamma distribution https://tminka.github.io/papers/minka-gamma.pdf
  107.  *      </li>
  108.  *      <li>
  109.  *          Ye, Z. S., and N. Chen (2017): Closed-Form Estimators for the Gamma Distribution Derived from
  110.  *              Likelihood Equations <i>The American Statistician</i> <b>71 (2)</b> 177-181
  111.  *      </li>
  112.  *  </ul>
  113.  *
  114.  *  <br><br>
  115.  *  <ul>
  116.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  117.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  118.  *      <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>
  119.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/dynamics/README.md">R<sup>1</sup> Gamma Distribution Implementation/Properties</a></li>
  120.  *  </ul>
  121.  *
  122.  * @author Lakshmi Krishnamurthy
  123.  */

  125. public class KullbackLieblerDivergence
  126. {

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

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

  156.         double k0 = 2.0;
  157.         double theta0 = 1.0;
  158.         int digammaTermCount = 1000;
  159.         double[] thetaArray =
  160.         {
  161.              1.0,
  162.              1.5,
  163.              2.0,
  164.              2.5,
  165.              3.0,
  166.         };
  167.         double[] kArray =
  168.         {
  169.              // 1,
  170.              1.0,
  171.              1.5,
  172.              2.0,
  173.              2.5,
  174.              3.0,
  175.              3.5,
  176.              4.0,
  177.         };

  179.         R1ToR1 gammaEstimator = new EulerIntegralSecondKind (
  180.             null
  181.         );

  183.         R2ToR1 lowerIncompleteGammaEstimator = LowerIncompleteGamma();

  185.         R1ToR1 digammaEstimator = CumulativeSeriesEstimator.AbramowitzStegun2007 (
  186.             digammaTermCount
  187.         );

  189.         R1ShapeScaleDistribution gammaDistribution0 = R1ShapeScaleDistribution.Standard (
  190.             k0,
  191.             theta0,
  192.             gammaEstimator,
  193.             digammaEstimator,
  194.             lowerIncompleteGammaEstimator
  195.         );

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

  199.         System.out.println ("\t|                                        GAMMA FUNCTION KULLBACK-LIEBLER DIVERGENCE ESTIMATE                                      ||");

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

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

  205.         System.out.println ("\t|                - Shape, Scale                                                                                                   ||");

  207.         System.out.println ("\t|                - Values for different s                                                                                         ||");

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

  211.         for (double theta : thetaArray)
  212.         {
  213.             for (double k : kArray)
  214.             {
  215.                 R1ShapeScaleDistribution gammaDistribution = R1ShapeScaleDistribution.Standard (
  216.                     k,
  217.                     theta,
  218.                     gammaEstimator,
  219.                     digammaEstimator,
  220.                     lowerIncompleteGammaEstimator
  221.                 );

  223.                 System.out.println (
  224.                     "\t| [" + FormatUtil.FormatDouble (k, 1, 1, 1., false) + ", " +
  225.                     FormatUtil.FormatDouble (theta, 1, 1, 1., false) +
  226.                     "] =>" + " " + FormatUtil.FormatDouble (
  227.                         R1ShapeScaleComposite.KullbackLieblerDivergence (
  228.                             gammaDistribution0,
  229.                             gammaDistribution
  230.                         ), 1, 6, 1., false
  231.                     ) + " ||"
  232.                 );
  233.             }
  234.         }

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

  238.         EnvManager.TerminateEnv();
  239.     }
  240. }
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