StandardExponentialTStatistic.java

package org.drip.sample.samplestatistics;

import org.drip.measure.continuous.R1UnivariateExponential;
import org.drip.measure.statistics.PopulationCentralMeasures;
import org.drip.measure.statistics.UnivariateMoments;
import org.drip.numerical.common.FormatUtil;
import org.drip.numerical.common.StringUtil;
import org.drip.service.env.EnvManager;

/*
 * -*- 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>StandardExponentialTStatistic</i> illustrates the Computation of the t-statistic, z-score, and other
 * related Metrics of the Sample/Population Mean 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>
 *          Wikipedia (2018): Probability Integral Transform
 *              https://en.wikipedia.org/wiki/Probability_integral_transform
 *      </li>
 *      <li>
 *          Wikipedia (2018): t-statistic https://en.wikipedia.org/wiki/T-statistic
 *      </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 StandardExponentialTStatistic
{

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

    private static final PopulationCentralMeasures PopulationMeasures()
    {
        return R1UnivariateExponential.Standard().populationCentralMeasures();
    }

    private static final double SampleMeanEstimate (
        final int count)
        throws Exception
    {
        double[] univariateRandomArray = new double[count];

        for (int index = 0; index < count; ++index)
        {
            univariateRandomArray[index] = UnivariateRandom();
        }

        return UnivariateMoments.Standard (
            StringUtil.GUID(),
            univariateRandomArray,
            null
        ).mean();
    }

    private static final UnivariateMoments SampleStatistics (
        final int drawCount,
        final int sampleCount)
        throws Exception
    {
        double[] sampleMeanEstimateArray = new double[sampleCount];

        for (int sampleIndex = 0; sampleIndex < sampleCount; ++sampleIndex)
        {
            sampleMeanEstimateArray[sampleIndex] = SampleMeanEstimate (drawCount);
        }

        return UnivariateMoments.Standard (
            StringUtil.GUID(),
            sampleMeanEstimateArray,
            null
        );
    }

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

        int drawCount = 10000;
        int sampleCount = 200;

        UnivariateMoments sampleStatistics = SampleStatistics (
            drawCount,
            sampleCount
        );

        PopulationCentralMeasures populationCentralMeasures = PopulationMeasures();

        double nextDraw = UnivariateRandom();

        double updatedMean = (sampleStatistics.mean() * sampleCount + nextDraw) / (sampleCount + 1);

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

        System.out.println ("\t|          STANDARD UNIFORM DISTRIBUTION           ||");

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

        System.out.println (
            "\t| Population Mean                => " +
            FormatUtil.FormatDouble (populationCentralMeasures.mean(), 1, 8, 1.)
        );

        System.out.println (
            "\t| Population Variance            => " +
            FormatUtil.FormatDouble (populationCentralMeasures.variance(), 1, 8, 1.)
        );

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

        System.out.println (
            "\t| Mean                           => " +
            FormatUtil.FormatDouble (sampleStatistics.mean(), 1, 8, 1.)
        );

        System.out.println (
            "\t| Variance                       => " +
            FormatUtil.FormatDouble (sampleStatistics.variance(), 1, 8, 1.)
        );

        System.out.println (
            "\t| Sample Count                   => " +
            FormatUtil.FormatDouble (sampleStatistics.numSample(), 3, 0, 1.)
        );

        System.out.println (
            "\t| Degrees Of Freedom             => " +
            FormatUtil.FormatDouble (sampleStatistics.degreesOfFreedom(), 3, 0, 1.)
        );

        System.out.println (
            "\t| Standard Deviation             => " +
            FormatUtil.FormatDouble (sampleStatistics.stdDev(), 1, 8, 1.)
        );

        System.out.println (
            "\t| Standard Error                 => " +
            FormatUtil.FormatDouble (sampleStatistics.stdError(), 1, 8, 1.)
        );

        System.out.println (
            "\t| Predictive Confidence Interval => " +
            FormatUtil.FormatDouble (sampleStatistics.predictiveConfidenceLevel(), 1, 8, 1.)
        );

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

        System.out.println (
            "\t| Next Draw                      => " +
            FormatUtil.FormatDouble (nextDraw, 1, 8, 1.)
        );

        System.out.println (
            "\t| Next Draw T-Statistics         => " +
            FormatUtil.FormatDouble (sampleStatistics.tStatistic (updatedMean), 1, 8, 1.)
        );

        System.out.println (
            "\t| Standard Error Offset          => " +
            FormatUtil.FormatDouble (sampleStatistics.standardErrorOffset (nextDraw), 1, 0, 1.)
        );

        System.out.println (
            "\t| Population Z-Score             => " +
            FormatUtil.FormatDouble (populationCentralMeasures.zScore (nextDraw), 1, 8, 1.)
        );

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

        EnvManager.TerminateEnv();
    }
}