DiscreteInverseGamma.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.R1ShapeScaleDiscrete;
  6. import org.drip.measure.statistics.UnivariateDiscreteThin;
  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>DiscreteInverseGamma</i> illustrates the Generation of Discrete Inverse Gamma Random Numbers using the
  89.  *  Ahlers-Dieter and the Marsaglia Schemes. 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 DiscreteInverseGamma
  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.     private static final void StatisticsArray (
  149.         final UnivariateDiscreteThin ahrensDieterThinStatistics,
  150.         final UnivariateDiscreteThin marsagliaThinStatistics)
  151.         throws Exception
  152.     {
  153.         System.out.println (
  154.             "\t| Average => " + FormatUtil.FormatDouble (
  155.                 ahrensDieterThinStatistics.average(), 2, 6, 1.
  156.             ) + " | " + FormatUtil.FormatDouble (
  157.                 marsagliaThinStatistics.average(), 2, 6, 1.
  158.             ) + " ||"
  159.         );

  161.         System.out.println (
  162.             "\t| Error   => " + FormatUtil.FormatDouble (
  163.                 ahrensDieterThinStatistics.error(), 2, 6, 1.
  164.             ) + " | " + FormatUtil.FormatDouble (
  165.                 marsagliaThinStatistics.error(), 2, 6, 1.
  166.             ) + " ||"
  167.         );

  169.         System.out.println (
  170.             "\t| Maximum => " + FormatUtil.FormatDouble (
  171.                 ahrensDieterThinStatistics.maximum(), 2, 6, 1.
  172.             ) + " | " + FormatUtil.FormatDouble (
  173.                 marsagliaThinStatistics.maximum(), 2, 6, 1.
  174.             ) + " ||"
  175.         );

  177.         System.out.println (
  178.             "\t| Minimum => " + FormatUtil.FormatDouble (
  179.                 ahrensDieterThinStatistics.minimum(), 2, 6, 1.
  180.             ) + " | " + FormatUtil.FormatDouble (
  181.                 marsagliaThinStatistics.minimum(), 2, 6, 1.
  182.             ) + " ||"
  183.         );
  184.     }

  186.     private static final void GenerateAndComputeStatistics (
  187.         final R1ToR1 gammaEstimator,
  188.         final R1ToR1 digammaEstimator,
  189.         final R2ToR1 lowerIncompleteGammaEstimator,
  190.         final double k,
  191.         final double theta,
  192.         final int simulationCount)
  193.         throws Exception
  194.     {
  195.         double[] marsagliaRandomArray = new double[simulationCount];
  196.         double[] ahrensDieterRandomArray = new double[simulationCount];

  198.         R1ShapeScaleDiscrete ahrensDieterGammaDiscrete = new R1ShapeScaleDiscrete (
  199.             k,
  200.             theta,
  201.             gammaEstimator,
  202.             digammaEstimator,
  203.             lowerIncompleteGammaEstimator,
  204.             R1ShapeScaleDiscrete.DISCRETE_RANDOM_FROM_AHRENS_DIETER
  205.         );

  207.         R1ShapeScaleDiscrete marsagilaGammaDiscrete = new R1ShapeScaleDiscrete (
  208.             k,
  209.             theta,
  210.             gammaEstimator,
  211.             digammaEstimator,
  212.             lowerIncompleteGammaEstimator,
  213.             R1ShapeScaleDiscrete.DISCRETE_RANDOM_FROM_MARSAGLIA
  214.         );

  216.         for (int simulationIndex = 0;
  217.             simulationIndex < simulationCount;
  218.             ++simulationIndex)
  219.         {
  220.             marsagliaRandomArray[simulationIndex] = ahrensDieterGammaDiscrete.randomInverseGamma();

  222.             ahrensDieterRandomArray[simulationIndex] = marsagilaGammaDiscrete.randomInverseGamma();
  223.         }

  225.         System.out.println (
  226.             "\t|-------------------------------------------------||" 
  227.         );

  229.         System.out.println (
  230.             "\t|      INVERSE GAMMA RANDOM NUMBER GENERATION     ||" 
  231.         );

  233.         System.out.println (
  234.             "\t|-------------------------------------------------||" 
  235.         );

  237.         System.out.println (
  238.             "\t|          k     => " + k
  239.         );

  241.         System.out.println (
  242.             "\t|          theta => " + theta
  243.         );

  245.         System.out.println (
  246.             "\t|-------------------------------------------------||" 
  247.         );

  249.         System.out.println (
  250.             "\t|          - Using Ahrens-Dieter (1982)           ||" 
  251.         );

  253.         System.out.println (
  254.             "\t|          - Using Marsaglia (1977)               ||" 
  255.         );

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

  261.         StatisticsArray (
  262.             new UnivariateDiscreteThin (
  263.                 ahrensDieterRandomArray
  264.             ),
  265.             new UnivariateDiscreteThin (
  266.                 marsagliaRandomArray
  267.             )
  268.         );

  270.         System.out.println (
  271.             "\t|-------------------------------------------------||" 
  272.         );

  274.         System.out.println();
  275.     }

  277.     public static final void main (
  278.         final String[] argumentArray)
  279.         throws Exception
  280.     {
  281.         EnvManager.InitEnv (
  282.             ""
  283.         );

  285.         double[] kArray = {
  286.             1.5,
  287.             1.0,
  288.             0.5,
  289.         };
  290.         double[] thetaArray = {
  291.             0.5,
  292.             1.0,
  293.             2.0,
  294.         };
  295.         int simulationCount = 100000;
  296.         int digammaTermCount = 1000;

  298.         R1ToR1 gammaEstimator = new EulerIntegralSecondKind (
  299.             null
  300.         );

  302.         R2ToR1 lowerIncompleteGammaEstimator = LowerIncompleteGamma();

  304.         R1ToR1 digammaEstimator = CumulativeSeriesEstimator.AbramowitzStegun2007 (
  305.             digammaTermCount
  306.         );

  308.         for (double k : kArray)
  309.         {
  310.             for (double theta : thetaArray)
  311.             {
  312.                 GenerateAndComputeStatistics (
  313.                     gammaEstimator,
  314.                     digammaEstimator,
  315.                     lowerIncompleteGammaEstimator,
  316.                     k,
  317.                     theta,
  318.                     simulationCount
  319.                 );
  320.             }
  321.         }

  323.         EnvManager.TerminateEnv();
  324.     }
  325. }
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