QQTest1.java

  1. package org.drip.sample.quantile;

  3. import org.drip.measure.gaussian.R1UnivariateNormal;
  4. import org.drip.numerical.common.FormatUtil;
  5. import org.drip.service.env.EnvManager;
  6. import org.drip.validation.evidence.Ensemble;
  7. import org.drip.validation.evidence.Sample;
  8. import org.drip.validation.evidence.TestStatisticEvaluator;
  9. import org.drip.validation.hypothesis.ProbabilityIntegralTransformTest;
  10. import org.drip.validation.quantile.PlottingPositionGeneratorHeuristic;
  11. import org.drip.validation.quantile.QQTestOutcome;
  12. import org.drip.validation.quantile.QQVertex;

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

  18. /*!
  19.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  20.  * 
  21.  *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
  22.  *      calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
  23.  *      FX, and structured products.
  24.  *  
  25.  *      https://lakshmidrip.github.io/DROP/
  26.  *  
  27.  *  DROP is composed of three main modules:
  28.  *  
  29.  *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
  30.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  31.  *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
  32.  * 
  33.  *  DROP Analytics Core implements libraries for the following:
  34.  *  - Fixed Income Analytics
  35.  *  - Asset Backed Analytics
  36.  *  - XVA Analytics
  37.  *  - Exposure and Margin Analytics
  38.  * 
  39.  *  DROP Portfolio Core implements libraries for the following:
  40.  *  - Asset Allocation Analytics
  41.  *  - Transaction Cost Analytics
  42.  * 
  43.  *  DROP Numerical Core implements libraries for the following:
  44.  *  - Statistical Learning Library
  45.  *  - Numerical Optimizer Library
  46.  *  - Machine Learning Library
  47.  *  - Spline Builder Library
  48.  * 
  49.  *  Documentation for DROP is Spread Over:
  50.  * 
  51.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  52.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  53.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  54.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  55.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  56.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  57.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  58.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  59.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  60.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  61.  * 
  62.  *  Licensed under the Apache License, Version 2.0 (the "License");
  63.  *      you may not use this file except in compliance with the License.
  64.  *   
  65.  *  You may obtain a copy of the License at
  66.  *      http://www.apache.org/licenses/LICENSE-2.0
  67.  *  
  68.  *  Unless required by applicable law or agreed to in writing, software
  69.  *      distributed under the License is distributed on an "AS IS" BASIS,
  70.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  71.  *  
  72.  *  See the License for the specific language governing permissions and
  73.  *      limitations under the License.
  74.  */

  76. /**
  77.  * <i>QQTest1</i> compares the Order Statistics between 2 Similar Normal Distributions using the Filliben
  78.  * (1975) Mean Based Plotting Position Generator.
  79.  *
  80.  *  <br><br>
  81.  *  <ul>
  82.  *      <li>
  83.  *          Gibbons, J. D., and S. Chakraborti (2003): <i>Non-parametric Statistical Inference 4th
  84.  *              Edition</i> <b>CRC Press</b>
  85.  *      </li>
  86.  *      <li>
  87.  *          Filliben, J. J. (1975): The Probability Plot Correlation Coefficient Test for Normality
  88.  *              <i>Technometrics, American Society for Quality</i> <b>17 (1)</b> 111-117
  89.  *      </li>
  90.  *      <li>
  91.  *          Gnanadesikan, R. (1977): <i>Methods for Statistical Analysis of Multivariate Observations</i>
  92.  *              <b>Wiley</b>
  93.  *      </li>
  94.  *      <li>
  95.  *          Thode, H. C. (2002): <i>Testing for Normality</i> <b>Marcel Dekker</b> New York
  96.  *      </li>
  97.  *      <li>
  98.  *          Wikipedia (2018): Q-Q Plot https://en.wikipedia.org/wiki/Q%E2%80%93Q_plot
  99.  *      </li>
  100.  *  </ul>
  101.  *
  102.  *  <br><br>
  103.  *  <ul>
  104.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/AnalyticsCore.md">Analytics Core Module</a></li>
  105.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ModelValidationAnalyticsLibrary.md">Model Validation Analytics Library</a></li>
  106.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/validation">Model Validation Suite</a></li>
  107.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/validation/quantile">Quantile Based Graphical Numerical Validators</a></li>
  108.  *  </ul>
  109.  * <br><br>
  110.  *
  111.  * @author Lakshmi Krishnamurthy
  112.  */

  114. public class QQTest1
  115. {

  117.     private static final double UnivariateRandom (
  118.         final double mean,
  119.         final double sigma)
  120.         throws Exception
  121.     {
  122.         return new R1UnivariateNormal (
  123.             mean,
  124.             sigma
  125.         ).random();
  126.     }

  128.     private static final Sample GenerateSample (
  129.         final double mean,
  130.         final double sigma,
  131.         final int drawCount)
  132.         throws Exception
  133.     {
  134.         double[] univariateRandomArray = new double[drawCount];

  136.         for (int drawIndex = 0; drawIndex < drawCount; ++drawIndex)
  137.         {
  138.             univariateRandomArray[drawIndex] = UnivariateRandom (
  139.                 mean,
  140.                 sigma
  141.             );
  142.         }

  144.         return new Sample (univariateRandomArray);
  145.     }

  147.     private static final Sample[] GenerateSampleArray (
  148.         final double mean,
  149.         final double sigma,
  150.         final int drawCount,
  151.         final int sampleCount)
  152.         throws Exception
  153.     {
  154.         Sample[] sampleArray = new Sample[sampleCount];

  156.         for (int sampleIndex = 0; sampleIndex < sampleCount; ++sampleIndex)
  157.         {
  158.             sampleArray[sampleIndex] = GenerateSample (
  159.                 mean,
  160.                 sigma,
  161.                 drawCount
  162.             );
  163.         }

  165.         return sampleArray;
  166.     }

  168.     private static final Ensemble GenerateEnsemble (
  169.         final double mean,
  170.         final double sigma,
  171.         final int drawCount,
  172.         final int sampleCount)
  173.         throws Exception
  174.     {
  175.         return new Ensemble (
  176.             GenerateSampleArray (
  177.                 mean,
  178.                 sigma,
  179.                 drawCount,
  180.                 sampleCount
  181.             ),
  182.             new TestStatisticEvaluator[]
  183.             {
  184.                 new TestStatisticEvaluator()
  185.                 {
  186.                     public double evaluate (
  187.                         final double[] drawArray)
  188.                         throws Exception
  189.                     {
  190.                         return 1.;
  191.                     }
  192.                 }
  193.             }
  194.         );
  195.     }

  197.     private static final void QQPlot (
  198.         final QQTestOutcome qqTestOutcome)
  199.         throws Exception
  200.     {
  201.         QQVertex[] qqVertexArray = qqTestOutcome.qqVertexArray();

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

  205.         System.out.println ("\t|          Q-Q TEST OUTCOME          ||");

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

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

  211.         System.out.println ("\t|        - Order Statistic Ordinal   ||");

  213.         System.out.println ("\t|        - Order Statistic Quantile  ||");

  215.         System.out.println ("\t|        - Order Statistic X         ||");

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

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

  221.         for (QQVertex qqVertex : qqVertexArray)
  222.         {
  223.             System.out.println (
  224.                 "\t| " + FormatUtil.FormatDouble (
  225.                     qqVertex.plottingPosition().orderStatisticOrdinal(), 2, 0, 1.
  226.                 ) + " => " +
  227.                 FormatUtil.FormatDouble (qqVertex.plottingPosition().quantile(), 1, 4, 1.) + " | " +
  228.                 FormatUtil.FormatDouble (qqVertex.orderStatisticX(), 1, 4, 1.) + " | " +
  229.                 FormatUtil.FormatDouble (qqVertex.orderStatisticY(), 1, 4, 1.) + " ||"
  230.             );
  231.         }

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

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

  237.         System.out.println (
  238.             "\t| Probability Plot Correlation Coefficient => " +
  239.             FormatUtil.FormatDouble (qqTestOutcome.probabilityPlotCorrelationCoefficient(), 1, 4, 1.) + " ||"
  240.         );

  242.         System.out.println ("\t|-----------------------------------------------------||");
  243.     }

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

  251.         int drawCount = 1000000;
  252.         int sampleCount = 1;
  253.         double sampleMean = 0.;
  254.         double hypothesisMean = 0.;
  255.         int orderStatisticCount = 25;
  256.         double sampleVolatility = 1.0;
  257.         double hypothesisVolatility = 0.5;

  259.         PlottingPositionGeneratorHeuristic plottingPositionGenerator =
  260.             PlottingPositionGeneratorHeuristic.Filliben1975 (orderStatisticCount);

  262.         Sample sample = GenerateSample (
  263.             sampleMean,
  264.             sampleVolatility,
  265.             drawCount
  266.         );

  268.         Ensemble hypothesis = GenerateEnsemble (
  269.             hypothesisMean,
  270.             hypothesisVolatility,
  271.             drawCount,
  272.             sampleCount
  273.         );

  275.         QQPlot (
  276.             new ProbabilityIntegralTransformTest (
  277.                 hypothesis.nativeProbabilityIntegralTransform()
  278.             ).qqTest (
  279.                 sample.nativeProbabilityIntegralTransform(),
  280.                 plottingPositionGenerator
  281.             )
  282.         );

  284.         EnvManager.TerminateEnv();
  285.     }
  286. }
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