StandardExponentialPIT.java

package org.drip.sample.samplestatistics;

import org.drip.measure.continuous.R1UnivariateExponential;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.validation.evidence.TestStatisticAccumulator;
import org.drip.validation.hypothesis.ProbabilityIntegralTransform;

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

/*!
 * Copyright (C) 2019 Lakshmi Krishnamurthy
 * 
 *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
 *      calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
 *      FX, and structured products.
 *  
 *      https://lakshmidrip.github.io/DROP/
 *  
 *  DROP is composed of three main modules:
 *  
 *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
 *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
 *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
 * 
 *  DROP Analytics Core implements libraries for the following:
 *  - Fixed Income Analytics
 *  - Asset Backed Analytics
 *  - XVA Analytics
 *  - Exposure and Margin Analytics
 * 
 *  DROP Portfolio Core implements libraries for the following:
 *  - Asset Allocation Analytics
 *  - Transaction Cost Analytics
 * 
 *  DROP Numerical Core implements libraries for the following:
 *  - Statistical Learning Library
 *  - Numerical Optimizer Library
 *  - Machine Learning Library
 *  - Spline Builder Library
 * 
 *  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
 *  - 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>StandardExponentialPIT</i> illustrates the Probability Integral Transform and the p-Value for an
 * Empirical Standard Exponential Distribution.
 *
 *  <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/AnalyticsCore.md">Analytics 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">Sample</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/hypothesistest">Statistical Hypothesis Tests</a></li>
 *  </ul>
 * <br><br>
 *
 * @author Lakshmi Krishnamurthy
 */

public class StandardExponentialPIT
{

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

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

        int pValueTestCount = 25;
        int instanceCount = 1000000;

        TestStatisticAccumulator responseAccumulator = new TestStatisticAccumulator();

        for (int instanceIndex = 0; instanceIndex < instanceCount; ++instanceIndex)
        {
            responseAccumulator.addTestStatistic (UnivariateRandom());
        }

        ProbabilityIntegralTransform pit = responseAccumulator.probabilityIntegralTransform();

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

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

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

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

        System.out.println ("\t|    Test Response  ||");

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

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

        for (int pValueTestIndex = 0; pValueTestIndex < pValueTestCount; ++pValueTestIndex)
        {
            double testResponse = UnivariateRandom();

            System.out.println (
                "\t|" +
                FormatUtil.FormatDouble (testResponse, 1, 4, 1.) + " => " +
                FormatUtil.FormatDouble (pit.pValue (testResponse), 1, 4, 1.) + " ||"
            );
        }

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

        EnvManager.TerminateEnv();
    }
}