ShapeScalePDFEstimate.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.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>ShapeScalePDFEstimate</i> demonstrates the Construction and Analysis of the R<sup>1</sup> Gamma
 *  Distribution using the Shape/Scale Parameterization. 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 ShapeScalePDFEstimate
{

    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
                );
            }
        };
    }

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

        int digammaTermCount = 1000;
        double[] thetaArray =
        {
             1.0,
             2.0,
             3.0,
             4.0,
             5.0,
        };
        double[] tArray =
        {
             0.1,
             1.0,
             2.0,
             3.0,
             4.0,
             5.0,
             6.0,
             7.0,
             8.0,
             9.0,
            10.0,
            12.0,
        };
        int[] kArray =
        {
             // 1,
             2,
             3,
             4,
             5,
             6,
             7,
             8,
        };
        double[] pValueArray =
        {
             0.05,
             0.10,
             0.15,
             0.20,
             0.25,
             0.30,
             0.35,
             0.40,
             0.45,
             0.50,
             0.55,
             0.60,
             0.65,
             0.70,
             0.75,
             0.80,
             0.85,
             0.90,
             0.95,
             0.99,
        };

        R1ToR1 gammaEstimator = new EulerIntegralSecondKind (
            null
        );

        R2ToR1 lowerIncompleteGammaEstimator = LowerIncompleteGamma();

        R1ToR1 digammaEstimator = CumulativeSeriesEstimator.AbramowitzStegun2007 (
            digammaTermCount
        );

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

        System.out.println ("\t|                                               PROBABILITY DENSITY FUNCTION ESTIMATE                                             ||");

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

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

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

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

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

        for (double theta : thetaArray)
        {
            for (int k : kArray)
            {
                R1ShapeScaleDistribution gammaDistribution = R1ShapeScaleDistribution.Standard (
                    k,
                    theta,
                    gammaEstimator,
                    digammaEstimator,
                    lowerIncompleteGammaEstimator
                );

                String display = "\t| [" +
                    FormatUtil.FormatDouble (k, 1, 0, 1., false) + ", " +
                    FormatUtil.FormatDouble (theta, 1, 0, 1., false) +
                "] =>";

                for (double t : tArray)
                {
                    display = display + " " + FormatUtil.FormatDouble (
                        gammaDistribution.density (
                            t
                        ), 1, 5, 1., false
                    ) + " |";
                }

                System.out.println (display + "|");
            }
        }

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

        System.out.println();

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

        System.out.println ("\t|                                             CUMULATIVE DISTRIBUTION FUNCTION ESTIMATE                                           ||");

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

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

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

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

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

        for (double theta : thetaArray)
        {
            for (int k : kArray)
            {
                R1ShapeScaleDistribution gammaDistribution = R1ShapeScaleDistribution.Standard (
                    k,
                    theta,
                    gammaEstimator,
                    digammaEstimator,
                    lowerIncompleteGammaEstimator
                );

                String display = "\t| [" +
                    FormatUtil.FormatDouble (k, 1, 0, 1., false) + ", " +
                    FormatUtil.FormatDouble (theta, 1, 0, 1., false) +
                "] =>";

                for (double t : tArray)
                {
                    display = display + " " + FormatUtil.FormatDouble (
                        gammaDistribution.cumulative (t), 1, 5, 1., false
                    ) + " |";
                }

                System.out.println (display + "|");
            }
        }

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

        System.out.println();

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

        System.out.println ("\t|                                         INVERSE CUMULATIVE DISTRIBUTION FUNCTION ESTIMATE                                       ||");

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

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

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

        System.out.println ("\t|                - Values for different p                                                                                         ||");

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

        for (double theta : thetaArray)
        {
            for (int k : kArray)
            {
                R1ShapeScaleDistribution gammaDistribution = R1ShapeScaleDistribution.Standard (
                    k,
                    theta,
                    gammaEstimator,
                    digammaEstimator,
                    lowerIncompleteGammaEstimator
                );

                String display = "\t| [" +
                    FormatUtil.FormatDouble (k, 1, 0, 1., false) + ", " +
                    FormatUtil.FormatDouble (theta, 1, 0, 1., false) +
                "] =>";

                for (double p : pValueArray)
                {
                    display = display + " " + FormatUtil.FormatDouble (
                        gammaDistribution.invCumulative (p), 1, 2, 1., false
                    ) + " |";
                }

                System.out.println (display + "|");
            }
        }

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

        EnvManager.TerminateEnv();
    }
}