MaximumLikelihoodInference.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.R1MaximumLikelihoodEstimator;
  6. import org.drip.measure.gamma.R1ParameterEstimator;
  7. import org.drip.measure.gamma.R1ShapeScaleDistribution;
  8. import org.drip.measure.gamma.ShapeScaleParameters;
  9. import org.drip.numerical.common.FormatUtil;
  10. import org.drip.service.env.EnvManager;
  11. import org.drip.specialfunction.digamma.CumulativeSeriesEstimator;
  12. import org.drip.specialfunction.gamma.EulerIntegralSecondKind;
  13. import org.drip.specialfunction.incompletegamma.LowerEulerIntegral;

  15. /*
  16.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  17.  */

  19. /*!
  20.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  21.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  22.  * 
  23.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  24.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  25.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  26.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  27.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  28.  *      and computational support.
  29.  *  
  30.  *      https://lakshmidrip.github.io/DROP/
  31.  *  
  32.  *  DROP is composed of three modules:
  33.  *  
  34.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  35.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  36.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  37.  * 
  38.  *  DROP Product Core implements libraries for the following:
  39.  *  - Fixed Income Analytics
  40.  *  - Loan Analytics
  41.  *  - Transaction Cost Analytics
  42.  * 
  43.  *  DROP Portfolio Core implements libraries for the following:
  44.  *  - Asset Allocation Analytics
  45.  *  - Asset Liability Management Analytics
  46.  *  - Capital Estimation Analytics
  47.  *  - Exposure Analytics
  48.  *  - Margin Analytics
  49.  *  - XVA Analytics
  50.  * 
  51.  *  DROP Computational Core implements libraries for the following:
  52.  *  - Algorithm Support
  53.  *  - Computation Support
  54.  *  - Function Analysis
  55.  *  - Model Validation
  56.  *  - Numerical Analysis
  57.  *  - Numerical Optimizer
  58.  *  - Spline Builder
  59.  *  - Statistical Learning
  60.  * 
  61.  *  Documentation for DROP is Spread Over:
  62.  * 
  63.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  64.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  65.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  66.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  67.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  68.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  69.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  70.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  71.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  72.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  73.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  74.  * 
  75.  *  Licensed under the Apache License, Version 2.0 (the "License");
  76.  *      you may not use this file except in compliance with the License.
  77.  *   
  78.  *  You may obtain a copy of the License at
  79.  *      http://www.apache.org/licenses/LICENSE-2.0
  80.  *  
  81.  *  Unless required by applicable law or agreed to in writing, software
  82.  *      distributed under the License is distributed on an "AS IS" BASIS,
  83.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  84.  *  
  85.  *  See the License for the specific language governing permissions and
  86.  *      limitations under the License.
  87.  */

  89. /**
  90.  * <i>MaximumLikelihoodInference</i> illustrates the Estimate of the Gamma Distribution from the Observation
  91.  *  Array using the Maximum Likelihood Estimator. The References are:
  92.  * 
  93.  * <br><br>
  94.  *  <ul>
  95.  *      <li>
  96.  *          Devroye, L. (1986): <i>Non-Uniform Random Variate Generation</i> <b>Springer-Verlag</b> New York
  97.  *      </li>
  98.  *      <li>
  99.  *          Gamma Distribution (2019): Gamma Distribution
  100.  *              https://en.wikipedia.org/wiki/Chi-squared_distribution
  101.  *      </li>
  102.  *      <li>
  103.  *          Louzada, F., P. L. Ramos, and E. Ramos (2019): A Note on Bias of Closed-Form Estimators for the
  104.  *              Gamma Distribution Derived From Likelihood Equations <i>The American Statistician</i> <b>73
  105.  *              (2)</b> 195-199
  106.  *      </li>
  107.  *      <li>
  108.  *          Minka, T. (2002): Estimating a Gamma distribution https://tminka.github.io/papers/minka-gamma.pdf
  109.  *      </li>
  110.  *      <li>
  111.  *          Ye, Z. S., and N. Chen (2017): Closed-Form Estimators for the Gamma Distribution Derived from
  112.  *              Likelihood Equations <i>The American Statistician</i> <b>71 (2)</b> 177-181
  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/measure/README.md">R<sup>d</sup> Continuous/Discrete Probability Measures</a></li>
  121.  *      <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>
  122.  *  </ul>
  123.  *
  124.  * @author Lakshmi Krishnamurthy
  125.  */

  127. public class MaximumLikelihoodInference
  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.     private static final double[] Generate (
  151.         final R1ToR1 gammaEstimator,
  152.         final R1ToR1 digammaEstimator,
  153.         final R2ToR1 lowerIncompleteGammaEstimator,
  154.         final double k,
  155.         final double theta,
  156.         final int simulationCount)
  157.         throws Exception
  158.     {
  159.         double[] marsagliaRandomArray = new double[simulationCount];

  161.         R1ShapeScaleDistribution gammaDistribution = R1ShapeScaleDistribution.Standard (
  162.             k,
  163.             theta,
  164.             gammaEstimator,
  165.             digammaEstimator,
  166.             lowerIncompleteGammaEstimator
  167.         );

  169.         for (int simulationIndex = 0;
  170.             simulationIndex < simulationCount;
  171.             ++simulationIndex)
  172.         {
  173.             marsagliaRandomArray[simulationIndex] = gammaDistribution.randomMarsaglia1977();
  174.         }

  176.         return marsagliaRandomArray;
  177.     }

  179.     public static final void main (
  180.         final String[] argumentArray)
  181.         throws Exception
  182.     {
  183.         EnvManager.InitEnv (
  184.             ""
  185.         );

  187.         double[] kArray = {
  188.             0.50,
  189.             1.00,
  190.             1.50,
  191.             2.00,
  192.             2.50,
  193.             3.00,
  194.             3.50,
  195.         };
  196.         double[] thetaArray = {
  197.             0.50,
  198.             1.00,
  199.             1.50,
  200.             2.00,
  201.             2.50,
  202.             3.00,
  203.             3.50,
  204.         };
  205.         int simulationCount = 100000;
  206.         int digammaTermCount = 1000;

  208.         R1ToR1 gammaEstimator = new EulerIntegralSecondKind (
  209.             null
  210.         );

  212.         R2ToR1 lowerIncompleteGammaEstimator = LowerIncompleteGamma();

  214.         R1ToR1 digammaEstimator = CumulativeSeriesEstimator.AbramowitzStegun2007 (
  215.             digammaTermCount
  216.         );

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

  220.         System.out.println ("\t|   SHAPE SCALE MLE INFERENCE    ||");

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

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

  226.         System.out.println ("\t|        IN => Shape             ||");

  228.         System.out.println ("\t|        IN => Scale             ||");

  230.         System.out.println ("\t|        OUT => Shape            ||");

  232.         System.out.println ("\t|        OUT => Scale            ||");

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

  236.         for (double k : kArray)
  237.         {
  238.             for (double theta : thetaArray)
  239.             {
  240.                 R1ParameterEstimator parameterEstimator =
  241.                     R1MaximumLikelihoodEstimator.FromRealizationArray (
  242.                         Generate (
  243.                             gammaEstimator,
  244.                             digammaEstimator,
  245.                             lowerIncompleteGammaEstimator,
  246.                             k,
  247.                             theta,
  248.                             simulationCount
  249.                         )
  250.                     );

  252.                 ShapeScaleParameters shapeScaleParameters = parameterEstimator.inferShapeScaleParameter();

  254.                 System.out.println (
  255.                     "\t| [" + FormatUtil.FormatDouble (k, 1, 2, 1., false) + " | " +
  256.                     FormatUtil.FormatDouble (theta, 1, 2, 1., false) + "] => {" +
  257.                     FormatUtil.FormatDouble (shapeScaleParameters.shape(), 1, 2, 1., false) + " | " +
  258.                     FormatUtil.FormatDouble (shapeScaleParameters.scale(), 1, 2, 1., false) + "} ||"
  259.                 );
  260.             }
  261.         }

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

  265.         EnvManager.TerminateEnv();
  266.     }
  267. }
Created with JaCoCo 0.7.9.201702052155