ExponentialAndersonDarlingGapAnalysis.java

package org.drip.sample.distancetest;

import org.drip.measure.continuous.R1UnivariateExponential;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.validation.distance.GapTestOutcome;
import org.drip.validation.distance.GapTestSetting;
import org.drip.validation.distance.GapLossWeightFunction;
import org.drip.validation.evidence.Ensemble;
import org.drip.validation.evidence.Sample;
import org.drip.validation.evidence.TestStatisticEvaluator;
import org.drip.validation.hypothesis.HistogramTestOutcome;
import org.drip.validation.hypothesis.HistogramTestSetting;
import org.drip.validation.hypothesis.ProbabilityIntegralTransformTest;
import org.drip.validation.quantile.PlottingPositionGenerator;
import org.drip.validation.quantile.PlottingPositionGeneratorHeuristic;

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

/*!
 * Copyright (C) 2020 Lakshmi Krishnamurthy
 * Copyright (C) 2019 Lakshmi Krishnamurthy
 * 
 *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
 *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
 *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
 *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
 *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
 *      and computational support.
 *  
 *      https://lakshmidrip.github.io/DROP/
 *  
 *  DROP is composed of three modules:
 *  
 *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
 *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
 *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
 * 
 *  DROP Product Core implements libraries for the following:
 *  - Fixed Income Analytics
 *  - Loan Analytics
 *  - Transaction Cost Analytics
 * 
 *  DROP Portfolio Core implements libraries for the following:
 *  - Asset Allocation Analytics
 *  - Asset Liability Management Analytics
 *  - Capital Estimation Analytics
 *  - Exposure Analytics
 *  - Margin Analytics
 *  - XVA Analytics
 * 
 *  DROP Computational Core implements libraries for the following:
 *  - Algorithm Support
 *  - Computation Support
 *  - Function Analysis
 *  - Model Validation
 *  - Numerical Analysis
 *  - Numerical Optimizer
 *  - Spline Builder
 *  - Statistical Learning
 * 
 *  Documentation for DROP is Spread Over:
 * 
 *  - Main                     => https://lakshmidrip.github.io/DROP/
 *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
 *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
 *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
 *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
 *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
 *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
 *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
 *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
 *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
 *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
 * 
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *      you may not use this file except in compliance with the License.
 *   
 *  You may obtain a copy of the License at
 *      http://www.apache.org/licenses/LICENSE-2.0
 *  
 *  Unless required by applicable law or agreed to in writing, software
 *      distributed under the License is distributed on an "AS IS" BASIS,
 *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  
 *  See the License for the specific language governing permissions and
 *      limitations under the License.
 */

/**
 * <i>ExponentialAndersonDarlingGapAnalysis</i> demonstrates the Generation of the Sample Distance Metrics
 * for Different Ensemble Hypotheses.
 * 
 *  <br><br>
 *  <ul>
 *      <li>
 *          <b>Reference Distribution  </b> - <i>Univariate Exponential</i>
 *      </li>
 *      <li>
 *          <b>Gap Loss Function       </b> - <i>Anfuso, Karyampas, and Nawroth (2017)</i>
 *      </li>
 *      <li>
 *          <b>Gap Loss Weight Function</b> - <i>Anderson and Darling</i>
 *      </li>
 *  </ul>
 *
 *  <br><br>
 *  <ul>
 *      <li>
 *          Anfuso, F., D. Karyampas, and A. Nawroth (2017): A Sound Basel III Compliant Framework for
 *              Back-testing Credit Exposure Models
 *              https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2264620 <b>eSSRN</b>
 *      </li>
 *      <li>
 *          Diebold, F. X., T. A. Gunther, and A. S. Tay (1998): Evaluating Density Forecasts with
 *              Applications to Financial Risk Management, International Economic Review 39 (4) 863-883
 *      </li>
 *      <li>
 *          Kenyon, C., and R. Stamm (2012): Discounting, LIBOR, CVA, and Funding: Interest Rate and Credit
 *              Pricing, Palgrave Macmillan
 *      </li>
 *      <li>
 *          Wikipedia (2018): Probability Integral Transform
 *              https://en.wikipedia.org/wiki/Probability_integral_transform
 *      </li>
 *      <li>
 *          Wikipedia (2019): p-value https://en.wikipedia.org/wiki/P-value
 *      </li>
 *  </ul>
 *
 *  <br><br>
 *  <ul>
 *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
 *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ModelValidationAnalyticsLibrary.md">Model Validation Analytics Library</a></li>
 *      <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>
 *      <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>
 *  </ul>
 * <br><br>
 *
 * @author Lakshmi Krishnamurthy
 */

public class ExponentialAndersonDarlingGapAnalysis
{

    private static final double UnivariateRandom (
        final double lambda)
        throws Exception
    {
        return new R1UnivariateExponential (lambda).random();
    }

    private static final Sample GenerateSample (
        final double lambda,
        final int drawCount)
        throws Exception
    {
        double[] univariateRandomArray = new double[drawCount];

        for (int drawIndex = 0; drawIndex < drawCount; ++drawIndex)
        {
            univariateRandomArray[drawIndex] = UnivariateRandom (lambda);
        }

        return new Sample (univariateRandomArray);
    }

    private static final Sample[] GenerateSampleArray (
        final double lambda,
        final int drawCount,
        final int sampleCount)
        throws Exception
    {
        Sample[] sampleArray = new Sample[sampleCount];

        for (int sampleIndex = 0; sampleIndex < sampleCount; ++sampleIndex)
        {
            sampleArray[sampleIndex] = GenerateSample (
                lambda,
                drawCount
            );
        }

        return sampleArray;
    }

    private static final Ensemble GenerateEnsemble (
        final double lambda,
        final int drawCount,
        final int sampleCount)
        throws Exception
    {
        return new Ensemble (
            GenerateSampleArray (
                lambda,
                drawCount,
                sampleCount
            ),
            new TestStatisticEvaluator[]
            {
                new TestStatisticEvaluator()
                {
                    public double evaluate (
                        final double[] drawArray)
                        throws Exception
                    {
                        return 1.;
                    }
                }
            }
        );
    }

    private static final GapTestOutcome DistanceTest (
        final Sample sample,
        final Ensemble ensemble,
        final GapTestSetting gapTestSetting)
        throws Exception
    {
        return new ProbabilityIntegralTransformTest (
            ensemble.nativeProbabilityIntegralTransform()
        ).distanceTest (
            sample.nativeProbabilityIntegralTransform(),
            gapTestSetting
        );
    }

    private static final void DistanceTest (
        final double hypothesisLambda,
        final int drawCount,
        final int sampleCount,
        final Sample sample,
        final GapTestSetting gapTestSetting,
        final PlottingPositionGenerator plottingPositionGenerator)
        throws Exception
    {
        Ensemble hypothesis = GenerateEnsemble (
            hypothesisLambda,
            drawCount,
            sampleCount
        );

        GapTestOutcome gapTestOutcome = DistanceTest (
            sample,
            hypothesis,
            gapTestSetting
        );

        HistogramTestOutcome histogram = new ProbabilityIntegralTransformTest (
            gapTestOutcome.probabilityIntegralTransformWeighted()
        ).histogramTest (
            HistogramTestSetting.AnfusoKaryampasNawroth2017 (
                plottingPositionGenerator
            )
        );

        double[] pValueIncrementalArray = histogram.pValueIncrementalArray();

        double[] pValueCumulativeArray = histogram.pValueCumulativeArray();

        double thresholdTestStatistic = histogram.thresholdTestStatistic();

        double[] gapArray = histogram.testStatisticArray();

        double distance = gapTestOutcome.distance();

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

        System.out.println ("\t|         Exponential Anfuso Karyampas Nawroth Distance Test         ||");

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

        System.out.println (
            "\t|   Lambda => [" + FormatUtil.FormatDouble (hypothesisLambda, 1, 8, 1.) +
            "]                                          ||"
        );


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

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

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

        System.out.println ("\t|        - Cumulative p-Value                                        ||");

        System.out.println ("\t|        - Incremental p-Value                                       ||");

        System.out.println ("\t|        - Ensemble Weighted Distance                                ||");

        System.out.println ("\t|        - p-Value Threshold Distance                                ||");

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

        for (int histogramIndex = 0;
            histogramIndex <= plottingPositionGenerator.orderStatisticCount() + 1;
            ++histogramIndex)
        {
            System.out.println (
                "\t|" +
                FormatUtil.FormatDouble (gapArray[histogramIndex], 1, 8, 1.) + " | " +
                FormatUtil.FormatDouble (pValueCumulativeArray[histogramIndex], 1, 8, 1.) + " | " +
                FormatUtil.FormatDouble (pValueIncrementalArray[histogramIndex], 1, 8, 1.) + " | " +
                FormatUtil.FormatDouble (distance, 1, 8, 1.) + " | " +
                FormatUtil.FormatDouble (thresholdTestStatistic, 1, 8, 1.) + " ||"
            );
        }

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

    public static final void main (
        final String[] argumentArray)
        throws Exception
    {
        EnvManager.InitEnv ("");

        int drawCount = 2000;
        int sampleCount = 600;
        double sampleLambda = 1.;
        int orderStatisticsCount = 20;
        double[] hypothesisLambdaArray =
        {
            0.20,
            0.30,
            0.40,
            0.50,
            0.60,
            0.70,
            0.80,
            0.90,
            1.00,
            1.10,
            1.20,
            1.30,
            1.40,
            1.50,
            1.60,
            1.70,
            1.80,
            1.90,
            2.00,
            2.10,
            2.20,
            2.30,
            2.40,
            2.50
        };

        GapTestSetting gapTestSetting = GapTestSetting.RiskFactorLossTest (
            GapLossWeightFunction.AndersonDarling()
        );

        Sample sample = GenerateSample (
            sampleLambda,
            drawCount
        );

        for (double hypothesisLambda : hypothesisLambdaArray)
        {
            DistanceTest (
                hypothesisLambda,
                drawCount,
                sampleCount,
                sample,
                gapTestSetting,
                PlottingPositionGeneratorHeuristic.NIST2013 (orderStatisticsCount)
            );
        }

        EnvManager.TerminateEnv();
    }
}