DiscreteRandomGenerationScheme.java

package org.drip.sample.gammadistribution;

import org.drip.function.definition.R1ToR1;
import org.drip.function.definition.R2ToR1;
import org.drip.measure.gamma.R1ShapeScaleDistribution;
import org.drip.measure.statistics.UnivariateDiscreteThin;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.specialfunction.digamma.CumulativeSeriesEstimator;
import org.drip.specialfunction.gamma.EulerIntegralSecondKind;
import org.drip.specialfunction.incompletegamma.LowerEulerIntegral;

/*
 * -*- 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>DiscreteRandomGenerationScheme</i> illustrates the Generation of Discrete Random Gamma Numbers
 *  following the R<sup>1</sup> Gamma Distribution using a variety of Schemes. The References are:
 * 
 * <br><br>
 *  <ul>
 *      <li>
 *          Devroye, L. (1986): <i>Non-Uniform Random Variate Generation</i> <b>Springer-Verlag</b> New York
 *      </li>
 *      <li>
 *          Gamma Distribution (2019): Gamma Distribution
 *              https://en.wikipedia.org/wiki/Chi-squared_distribution
 *      </li>
 *      <li>
 *          Louzada, F., P. L. Ramos, and E. Ramos (2019): A Note on Bias of Closed-Form Estimators for the
 *              Gamma Distribution Derived From Likelihood Equations <i>The American Statistician</i> <b>73
 *              (2)</b> 195-199
 *      </li>
 *      <li>
 *          Minka, T. (2002): Estimating a Gamma distribution https://tminka.github.io/papers/minka-gamma.pdf
 *      </li>
 *      <li>
 *          Ye, Z. S., and N. Chen (2017): Closed-Form Estimators for the Gamma Distribution Derived from
 *              Likelihood Equations <i>The American Statistician</i> <b>71 (2)</b> 177-181
 *      </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/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/README.md">R<sup>d</sup> Continuous/Discrete Probability Measures</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/dynamics/README.md">R<sup>1</sup> Gamma Distribution Implementation/Properties</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class DiscreteRandomGenerationScheme
{

    private static final R2ToR1 LowerIncompleteGamma()
        throws Exception
    {
        return new R2ToR1()
        {
            @Override public double evaluate (
                final double s,
                final double t)
                throws Exception
            {
                return new LowerEulerIntegral (
                    null,
                    t
                ).evaluate (
                    s
                );
            }
        };
    }

    private static final void StatisticsArray (
        final UnivariateDiscreteThin inverseCDFThinStatistics,
        final UnivariateDiscreteThin ahrensDieterThinStatistics,
        final UnivariateDiscreteThin marsagliaThinStatistics)
        throws Exception
    {
        System.out.println (
            "\t| Average => " + FormatUtil.FormatDouble (
                inverseCDFThinStatistics.average(), 2, 6, 1.
            ) + " | " + FormatUtil.FormatDouble (
                ahrensDieterThinStatistics.average(), 2, 6, 1.
            ) + " | " + FormatUtil.FormatDouble (
                marsagliaThinStatistics.average(), 2, 6, 1.
            ) + " ||"
        );

        System.out.println (
            "\t| Error   => " + FormatUtil.FormatDouble (
                inverseCDFThinStatistics.error(), 2, 6, 1.
            ) + " | " + FormatUtil.FormatDouble (
                ahrensDieterThinStatistics.error(), 2, 6, 1.
            ) + " | " + FormatUtil.FormatDouble (
                marsagliaThinStatistics.error(), 2, 6, 1.
            ) + " ||"
        );

        System.out.println (
            "\t| Maximum => " + FormatUtil.FormatDouble (
                inverseCDFThinStatistics.maximum(), 2, 6, 1.
            ) + " | " + FormatUtil.FormatDouble (
                ahrensDieterThinStatistics.maximum(), 2, 6, 1.
            ) + " | " + FormatUtil.FormatDouble (
                marsagliaThinStatistics.maximum(), 2, 6, 1.
            ) + " ||"
        );

        System.out.println (
            "\t| Minimum => " + FormatUtil.FormatDouble (
                inverseCDFThinStatistics.minimum(), 2, 6, 1.
            ) + " | " + FormatUtil.FormatDouble (
                ahrensDieterThinStatistics.minimum(), 2, 6, 1.
            ) + " | " + FormatUtil.FormatDouble (
                marsagliaThinStatistics.minimum(), 2, 6, 1.
            ) + " ||"
        );
    }

    private static final void StatisticsArray2 (
        final UnivariateDiscreteThin ahrensDieterThinStatistics,
        final UnivariateDiscreteThin marsagliaThinStatistics)
        throws Exception
    {
        System.out.println (
            "\t| Average => " + FormatUtil.FormatDouble (
                ahrensDieterThinStatistics.average(), 2, 6, 1.
            ) + " | " + FormatUtil.FormatDouble (
                marsagliaThinStatistics.average(), 2, 6, 1.
            ) + " ||"
        );

        System.out.println (
            "\t| Error   => " + FormatUtil.FormatDouble (
                ahrensDieterThinStatistics.error(), 2, 6, 1.
            ) + " | " + FormatUtil.FormatDouble (
                marsagliaThinStatistics.error(), 2, 6, 1.
            ) + " ||"
        );

        System.out.println (
            "\t| Maximum => " + FormatUtil.FormatDouble (
                ahrensDieterThinStatistics.maximum(), 2, 6, 1.
            ) + " | " + FormatUtil.FormatDouble (
                marsagliaThinStatistics.maximum(), 2, 6, 1.
            ) + " ||"
        );

        System.out.println (
            "\t| Minimum => " + FormatUtil.FormatDouble (
                ahrensDieterThinStatistics.minimum(), 2, 6, 1.
            ) + " | " + FormatUtil.FormatDouble (
                marsagliaThinStatistics.minimum(), 2, 6, 1.
            ) + " ||"
        );
    }

    private static final void GenerateAndComputeStatistics (
        final R1ToR1 gammaEstimator,
        final R1ToR1 digammaEstimator,
        final R2ToR1 lowerIncompleteGammaEstimator,
        final double k,
        final double theta,
        final int simulationCount)
        throws Exception
    {
        double[] marsagliaRandomArray = new double[simulationCount];
        double[] inverseCDFRandomArray = new double[simulationCount];
        double[] ahrensDieterRandomArray = new double[simulationCount];

        R1ShapeScaleDistribution gammaDistribution = R1ShapeScaleDistribution.Standard (
            k,
            theta,
            gammaEstimator,
            digammaEstimator,
            lowerIncompleteGammaEstimator
        );

        for (int simulationIndex = 0;
            simulationIndex < simulationCount;
            ++simulationIndex)
        {
            if (k > 1)
            {
                inverseCDFRandomArray[simulationIndex] = gammaDistribution.random();
            }

            marsagliaRandomArray[simulationIndex] = gammaDistribution.randomMarsaglia1977();

            ahrensDieterRandomArray[simulationIndex] = gammaDistribution.randomAhrensDieter1982();
        }

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

        System.out.println (
            "\t|          GAMMA RANDOM NUMBER GENERATION         ||" 
        );

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

        System.out.println (
            "\t|          k     => " + k
        );

        System.out.println (
            "\t|          theta => " + theta
        );

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

        if (k > 1)
        {
            System.out.println (
                "\t|          - From Uniform CDF                     ||" 
            );

            System.out.println (
                "\t|          - Using Ahrens-Dieter (1982)           ||" 
            );

            System.out.println (
                "\t|          - Using Marsaglia (1977)               ||" 
            );

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

            StatisticsArray (
                new UnivariateDiscreteThin (
                    inverseCDFRandomArray
                ),
                new UnivariateDiscreteThin (
                    ahrensDieterRandomArray
                ),
                new UnivariateDiscreteThin (
                    marsagliaRandomArray
                )
            );
        }
        else
        {
            System.out.println (
                "\t|          - Using Ahrens-Dieter (1982)           ||" 
            );

            System.out.println (
                "\t|          - Using Marsaglia (1977)               ||" 
            );

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

            StatisticsArray2 (
                new UnivariateDiscreteThin (
                    ahrensDieterRandomArray
                ),
                new UnivariateDiscreteThin (
                    marsagliaRandomArray
                )
            );
        }

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

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

        double[] kArray = {
            1.5,
            0.5,
        };
        double[] thetaArray = {
            2.0,
        };
        int simulationCount = 1000;
        int digammaTermCount = 1000;

        R1ToR1 gammaEstimator = new EulerIntegralSecondKind (
            null
        );

        R2ToR1 lowerIncompleteGammaEstimator = LowerIncompleteGamma();

        R1ToR1 digammaEstimator = CumulativeSeriesEstimator.AbramowitzStegun2007 (
            digammaTermCount
        );

        for (double k : kArray)
        {
            for (double theta : thetaArray)
            {
                GenerateAndComputeStatistics (
                    gammaEstimator,
                    digammaEstimator,
                    lowerIncompleteGammaEstimator,
                    k,
                    theta,
                    simulationCount
                );
            }
        }

        EnvManager.TerminateEnv();
    }
}