ExponentialAndersonDarlingGapDiscriminant.java

  1. package org.drip.sample.distancetest;

  3. import org.drip.measure.continuous.R1UnivariateExponential;
  4. import org.drip.numerical.common.FormatUtil;
  5. import org.drip.service.env.EnvManager;
  6. import org.drip.validation.distance.GapTestOutcome;
  7. import org.drip.validation.distance.GapTestSetting;
  8. import org.drip.validation.distance.GapLossWeightFunction;
  9. import org.drip.validation.evidence.Ensemble;
  10. import org.drip.validation.evidence.Sample;
  11. import org.drip.validation.evidence.TestStatisticEvaluator;
  12. import org.drip.validation.hypothesis.ProbabilityIntegralTransformTest;

  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>ExponentialAndersonDarlingGapDiscriminant</i> demonstrates the Generation of the Sample Distance
  90.  * Discriminant Metrics for Different Ensemble Hypotheses.
  91.  * 
  92.  *  <br><br>
  93.  *  <ul>
  94.  *      <li>
  95.  *          <b>Reference Distribution  </b> - <i>Univariate Exponential</i>
  96.  *      </li>
  97.  *      <li>
  98.  *          <b>Gap Loss Function       </b> - <i>Anfuso, Karyampas, and Nawroth (2017)</i>
  99.  *      </li>
  100.  *      <li>
  101.  *          <b>Gap Loss Weight Function</b> - <i>Anderson and Darling</i>
  102.  *      </li>
  103.  *  </ul>
  104.  *
  105.  *  <br><br>
  106.  *  <ul>
  107.  *      <li>
  108.  *          Anfuso, F., D. Karyampas, and A. Nawroth (2017): A Sound Basel III Compliant Framework for
  109.  *              Back-testing Credit Exposure Models
  110.  *              https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2264620 <b>eSSRN</b>
  111.  *      </li>
  112.  *      <li>
  113.  *          Diebold, F. X., T. A. Gunther, and A. S. Tay (1998): Evaluating Density Forecasts with
  114.  *              Applications to Financial Risk Management, International Economic Review 39 (4) 863-883
  115.  *      </li>
  116.  *      <li>
  117.  *          Kenyon, C., and R. Stamm (2012): Discounting, LIBOR, CVA, and Funding: Interest Rate and Credit
  118.  *              Pricing, Palgrave Macmillan
  119.  *      </li>
  120.  *      <li>
  121.  *          Wikipedia (2018): Probability Integral Transform
  122.  *              https://en.wikipedia.org/wiki/Probability_integral_transform
  123.  *      </li>
  124.  *      <li>
  125.  *          Wikipedia (2019): p-value https://en.wikipedia.org/wiki/P-value
  126.  *      </li>
  127.  *  </ul>
  128.  *
  129.  *  <br><br>
  130.  *  <ul>
  131.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  132.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ModelValidationAnalyticsLibrary.md">Model Validation Analytics Library</a></li>
  133.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">DROP API Construction and Usage</a></li>
  134.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/validation">Empirical Univariate Gap Distance Tests</a></li>
  135.  *  </ul>
  136.  * <br><br>
  137.  *
  138.  * @author Lakshmi Krishnamurthy
  139.  */

  141. public class ExponentialAndersonDarlingGapDiscriminant
  142. {

  144.     private static final double UnivariateRandom (
  145.         final double lambda)
  146.         throws Exception
  147.     {
  148.         return new R1UnivariateExponential (lambda).random();
  149.     }

  151.     private static final Sample GenerateSample (
  152.         final double lambda,
  153.         final int drawCount)
  154.         throws Exception
  155.     {
  156.         double[] univariateRandomArray = new double[drawCount];

  158.         for (int drawIndex = 0; drawIndex < drawCount; ++drawIndex)
  159.         {
  160.             univariateRandomArray[drawIndex] = UnivariateRandom (lambda);
  161.         }

  163.         return new Sample (univariateRandomArray);
  164.     }

  166.     private static final Sample[] GenerateSampleArray (
  167.         final double lambda,
  168.         final int drawCount,
  169.         final int sampleCount)
  170.         throws Exception
  171.     {
  172.         Sample[] sampleArray = new Sample[sampleCount];

  174.         for (int sampleIndex = 0; sampleIndex < sampleCount; ++sampleIndex)
  175.         {
  176.             sampleArray[sampleIndex] = GenerateSample (
  177.                 lambda,
  178.                 drawCount
  179.             );
  180.         }

  182.         return sampleArray;
  183.     }

  185.     private static final Ensemble GenerateEnsemble (
  186.         final double lambda,
  187.         final int drawCount,
  188.         final int sampleCount)
  189.         throws Exception
  190.     {
  191.         return new Ensemble (
  192.             GenerateSampleArray (
  193.                 lambda,
  194.                 drawCount,
  195.                 sampleCount
  196.             ),
  197.             new TestStatisticEvaluator[]
  198.             {
  199.                 new TestStatisticEvaluator()
  200.                 {
  201.                     public double evaluate (
  202.                         final double[] drawArray)
  203.                         throws Exception
  204.                     {
  205.                         return 1.;
  206.                     }
  207.                 }
  208.             }
  209.         );
  210.     }

  212.     private static final GapTestOutcome DistanceTest (
  213.         final Sample sample,
  214.         final Ensemble ensemble,
  215.         final GapTestSetting gapTestSetting)
  216.         throws Exception
  217.     {
  218.         return new ProbabilityIntegralTransformTest (
  219.             ensemble.nativeProbabilityIntegralTransform()
  220.         ).distanceTest (
  221.             sample.nativeProbabilityIntegralTransform(),
  222.             gapTestSetting
  223.         );
  224.     }

  226.     private static final double DistanceTest (
  227.         final double hypothesisLambda,
  228.         final int drawCount,
  229.         final int sampleCount,
  230.         final Sample sample,
  231.         final GapTestSetting gapTestSetting)
  232.         throws Exception
  233.     {
  234.         return DistanceTest (
  235.             sample,
  236.             GenerateEnsemble (
  237.                 hypothesisLambda,
  238.                 drawCount,
  239.                 sampleCount
  240.             ),
  241.             gapTestSetting
  242.         ).distance();
  243.     }

  245.     public static final void main (
  246.         final String[] argumentArray)
  247.         throws Exception
  248.     {
  249.         EnvManager.InitEnv ("");

  251.         int drawCount = 2000;
  252.         int sampleCount = 600;
  253.         double sampleLambda = 1.;
  254.         double[] hypothesisLambdaArray =
  255.         {
  256.             0.20,
  257.             0.30,
  258.             0.40,
  259.             0.50,
  260.             0.60,
  261.             0.70,
  262.             0.80,
  263.             0.90,
  264.             1.00,
  265.             1.10,
  266.             1.20,
  267.             1.30,
  268.             1.40,
  269.             1.50,
  270.             1.60,
  271.             1.70,
  272.             1.80,
  273.             1.90,
  274.             2.00,
  275.             2.10,
  276.             2.20,
  277.             2.30,
  278.             2.40,
  279.             2.50
  280.         };

  282.         GapTestSetting gapTestSetting = GapTestSetting.RiskFactorLossTest (
  283.             GapLossWeightFunction.AndersonDarling()
  284.         );

  286.         Sample sample = GenerateSample (
  287.             sampleLambda,
  288.             drawCount
  289.         );

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

  293.         System.out.println ("\t|    DISCRIMINANT GRID SCAN    ||");

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

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

  299.         System.out.println ("\t|        - Hypothesis Lambda   ||");

  301.         System.out.println ("\t|        - Distance Metric     ||");

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

  305.         for (double hypothesisLambda : hypothesisLambdaArray)
  306.         {
  307.             System.out.println (
  308.                 "\t| " +
  309.                 FormatUtil.FormatDouble (hypothesisLambda, 1, 2, 1.) + " => " +
  310.                 FormatUtil.FormatDouble (
  311.                     DistanceTest (
  312.                         hypothesisLambda,
  313.                         drawCount,
  314.                         sampleCount,
  315.                         sample,
  316.                         gapTestSetting
  317.                     ),
  318.                     1, 8, 1.
  319.                 ) + "         ||"
  320.             );
  321.         }

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

  325.         EnvManager.TerminateEnv();
  326.     }
  327. }
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