CentralPDFEstimate.java

package org.drip.sample.chisquaredistribution;

import org.drip.function.definition.R1ToR1;
import org.drip.function.definition.R2ToR1;
import org.drip.measure.chisquare.R1Central;
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>CentralPDFEstimate</i> illustrates the Construction and the Usage of a Central Chi-squared
 * Distribution. The References are:
 * 
 * <br><br>
 *  <ul>
 *      <li>
 *          Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
 *              on Mathematics</b>
 *      </li>
 *      <li>
 *          Backstrom, T., and J. Fischer (2018): Fast Randomization for Distributed Low Bit-rate Coding of
 *              Speech and Audio <i>IEEE/ACM Transactions on Audio, Speech, and Language Processing</i> <b>26
 *              (1)</b> 19-30
 *      </li>
 *      <li>
 *          Chi-Squared Distribution (2019): Chi-Squared Function
 *              https://en.wikipedia.org/wiki/Chi-squared_distribution
 *      </li>
 *      <li>
 *          Johnson, N. L., S. Kotz, and N. Balakrishnan (1994): <i>Continuous Univariate Distributions
 *              2<sup>nd</sup> Edition</i> <b>John Wiley and Sons</b>
 *      </li>
 *      <li>
 *          National Institute of Standards and Technology (2019): Chi-Squared Distribution
 *              https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm
 *      </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/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/chisquaredistribution/README.md">Chi-Square Distribution Usage/Properties</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class CentralPDFEstimate
{

    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[] 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[] dofArray =
        {
             // 1,
             2,
             3,
             4,
             5,
             6,
             7,
             8,
             9,
        };
        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,
        };

        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|                - Degrees of Freedom                                                                                          ||");

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

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

        for (int dof : dofArray)
        {
            R1Central r1UnivariateScaledExponential = new R1Central (
                dof,
                gammaEstimator,
                digammaEstimator,
                lowerIncompleteGammaEstimator
            );

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

            for (double t : tArray)
            {
                display = display + " " + FormatUtil.FormatDouble (
                    r1UnivariateScaledExponential.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|                - Degrees of Freedom                                                                                          ||");

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

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

        for (int dof : dofArray)
        {
            R1Central r1UnivariateScaledExponential = new R1Central (
                dof,
                gammaEstimator,
                digammaEstimator,
                lowerIncompleteGammaEstimator
            );

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

            for (double t : tArray)
            {
                display = display + " " + FormatUtil.FormatDouble (
                    r1UnivariateScaledExponential.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|                - Degrees of Freedom                                                                                          ||");

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

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

        for (int dof : dofArray)
        {
            R1Central r1UnivariateScaledExponential = new R1Central (
                dof,
                gammaEstimator,
                digammaEstimator,
                lowerIncompleteGammaEstimator
            );

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

            for (double p : pValueArray)
            {
                display = display + " " + FormatUtil.FormatDouble (
                    r1UnivariateScaledExponential.invCumulative (p), 1, 5, 1., false
                ) + " |";
            }

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

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

        EnvManager.TerminateEnv();
    }
}