ConsistentInference.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.R1ConsistentEstimator;
  6. import org.drip.measure.gamma.R1ShapeScaleDistribution;
  7. import org.drip.measure.gamma.ShapeScaleParameters;
  8. import org.drip.numerical.common.FormatUtil;
  9. import org.drip.service.env.EnvManager;
  10. import org.drip.specialfunction.digamma.CumulativeSeriesEstimator;
  11. import org.drip.specialfunction.gamma.EulerIntegralSecondKind;
  12. import org.drip.specialfunction.incompletegamma.LowerEulerIntegral;

  14. /*
  15.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  16.  */

  18. /*!
  19.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  20.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  21.  * 
  22.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  23.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  24.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  25.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  26.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  27.  *      and computational support.
  28.  *  
  29.  *      https://lakshmidrip.github.io/DROP/
  30.  *  
  31.  *  DROP is composed of three modules:
  32.  *  
  33.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  34.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  35.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  36.  * 
  37.  *  DROP Product Core implements libraries for the following:
  38.  *  - Fixed Income Analytics
  39.  *  - Loan Analytics
  40.  *  - Transaction Cost Analytics
  41.  * 
  42.  *  DROP Portfolio Core implements libraries for the following:
  43.  *  - Asset Allocation Analytics
  44.  *  - Asset Liability Management Analytics
  45.  *  - Capital Estimation Analytics
  46.  *  - Exposure Analytics
  47.  *  - Margin Analytics
  48.  *  - XVA Analytics
  49.  * 
  50.  *  DROP Computational Core implements libraries for the following:
  51.  *  - Algorithm Support
  52.  *  - Computation Support
  53.  *  - Function Analysis
  54.  *  - Model Validation
  55.  *  - Numerical Analysis
  56.  *  - Numerical Optimizer
  57.  *  - Spline Builder
  58.  *  - Statistical Learning
  59.  * 
  60.  *  Documentation for DROP is Spread Over:
  61.  * 
  62.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  63.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  64.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  65.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  66.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  67.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  68.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  69.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  70.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  71.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  72.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  73.  * 
  74.  *  Licensed under the Apache License, Version 2.0 (the "License");
  75.  *      you may not use this file except in compliance with the License.
  76.  *   
  77.  *  You may obtain a copy of the License at
  78.  *      http://www.apache.org/licenses/LICENSE-2.0
  79.  *  
  80.  *  Unless required by applicable law or agreed to in writing, software
  81.  *      distributed under the License is distributed on an "AS IS" BASIS,
  82.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  83.  *  
  84.  *  See the License for the specific language governing permissions and
  85.  *      limitations under the License.
  86.  */

  88. /**
  89.  * <i>ConsistentInference</i> illustrates the Estimate of the Gamma Distribution from the Observation Array
  90.  *  using the Consistent Closed-Form Estimator. The References are:
  91.  * 
  92.  * <br><br>
  93.  *  <ul>
  94.  *      <li>
  95.  *          Devroye, L. (1986): <i>Non-Uniform Random Variate Generation</i> <b>Springer-Verlag</b> New York
  96.  *      </li>
  97.  *      <li>
  98.  *          Gamma Distribution (2019): Gamma Distribution
  99.  *              https://en.wikipedia.org/wiki/Chi-squared_distribution
  100.  *      </li>
  101.  *      <li>
  102.  *          Louzada, F., P. L. Ramos, and E. Ramos (2019): A Note on Bias of Closed-Form Estimators for the
  103.  *              Gamma Distribution Derived From Likelihood Equations <i>The American Statistician</i> <b>73
  104.  *              (2)</b> 195-199
  105.  *      </li>
  106.  *      <li>
  107.  *          Minka, T. (2002): Estimating a Gamma distribution https://tminka.github.io/papers/minka-gamma.pdf
  108.  *      </li>
  109.  *      <li>
  110.  *          Ye, Z. S., and N. Chen (2017): Closed-Form Estimators for the Gamma Distribution Derived from
  111.  *              Likelihood Equations <i>The American Statistician</i> <b>71 (2)</b> 177-181
  112.  *      </li>
  113.  *  </ul>
  114.  *
  115.  *  <br><br>
  116.  *  <ul>
  117.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  118.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  119.  *      <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>
  120.  *      <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>
  121.  *  </ul>
  122.  *
  123.  * @author Lakshmi Krishnamurthy
  124.  */

  126. public class ConsistentInference
  127. {

  129.     private static final R2ToR1 LowerIncompleteGamma()
  130.         throws Exception
  131.     {
  132.         return new R2ToR1()
  133.         {
  134.             @Override public double evaluate (
  135.                 final double s,
  136.                 final double t)
  137.                 throws Exception
  138.             {
  139.                 return new LowerEulerIntegral (
  140.                     null,
  141.                     t
  142.                 ).evaluate (
  143.                     s
  144.                 );
  145.             }
  146.         };
  147.     }

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

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

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

  175.         return marsagliaRandomArray;
  176.     }

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

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

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

  211.         R2ToR1 lowerIncompleteGammaEstimator = LowerIncompleteGamma();

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

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

  219.         System.out.println ("\t|        SHAPE SCALE CONSISTENT INFERENCE        ||");

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

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

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

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

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

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

  233.         System.out.println ("\t|        OUT => Shape Bias Correction Factor     ||");

  235.         System.out.println ("\t|        OUT => Scale Bias Adjustment            ||");

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

  239.         for (double k : kArray)
  240.         {
  241.             for (double theta : thetaArray)
  242.             {
  243.                 R1ConsistentEstimator consistentEstimator =
  244.                     R1ConsistentEstimator.FromRealizationArray (
  245.                         Generate (
  246.                             gammaEstimator,
  247.                             digammaEstimator,
  248.                             lowerIncompleteGammaEstimator,
  249.                             k,
  250.                             theta,
  251.                             simulationCount
  252.                         )
  253.                     );

  255.                 ShapeScaleParameters shapeScaleParameters = consistentEstimator.inferShapeScaleParameter();

  257.                 System.out.println (
  258.                     "\t| [" + FormatUtil.FormatDouble (k, 1, 2, 1., false) + " | " +
  259.                     FormatUtil.FormatDouble (theta, 1, 2, 1., false) + "] => {" +
  260.                     FormatUtil.FormatDouble (shapeScaleParameters.shape(), 1, 2, 1., false) + " | " +
  261.                     FormatUtil.FormatDouble (shapeScaleParameters.scale(), 1, 2, 1., false) + "} | {" +
  262.                     FormatUtil.FormatDouble (
  263.                         consistentEstimator.shapeBiasCorrectionAdjustment (
  264.                             shapeScaleParameters.shape()
  265.                         ), 1, 2, 1., false
  266.                     ) + " | " +
  267.                     FormatUtil.FormatDouble (
  268.                         consistentEstimator.scaleBiasCorrectionFactor(), 1, 2, 1., false
  269.                     ) + "} ||"
  270.                 );
  271.             }
  272.         }

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

  276.         EnvManager.TerminateEnv();
  277.     }
  278. }
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