KohlrauschPDFEstimate.java

package org.drip.sample.scaledexponential;

import org.drip.function.definition.R1ToR1;
import org.drip.measure.continuous.R1UnivariateScaledExponential;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.specialfunction.definition.ScaledExponentialEstimator;
import org.drip.specialfunction.gamma.EulerIntegralSecondKind;

/*
 * -*- 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>KohlrauschPDFEstimate</i> illustrates the Construction and Usage of the Kohlrausch PDF Estimate
 * Function. The References are:
 * 
 * <br><br>
 *  <ul>
 *      <li>
 *          Gradshteyn, I. S., I. M. Ryzhik, Y. V. Geronimus, M. Y. Tseytlin, and A. Jeffrey (2015):
 *              <i>Tables of Integrals, Series, and Products</i> <b>Academic Press</b>
 *      </li>
 *      <li>
 *          Hilfer, J. (2002): H-function Representations for Stretched Exponential Relaxation and non-Debye
 *              Susceptibilities in Glassy Systems <i>Physical Review E</i> <b>65 (6)</b> 061510
 *      </li>
 *      <li>
 *          Wikipedia (2019): Stretched Exponential Function
 *              https://en.wikipedia.org/wiki/Stretched_exponential_function
 *      </li>
 *      <li>
 *          Wuttke, J. (2012): Laplace-Fourier Transform of the Stretched Exponential Function: Analytic
 *              Error-Bounds, Double Exponential Transform, and Open Source Implementation <i>libkw</i>
 *              <i>Algorithm</i> <b>5 (4)</b> 604-628
 *      </li>
 *      <li>
 *          Zorn, R. (2002): Logarithmic Moments of Relaxation Time Distributions <i>Journal of Chemical
 *              Physics</i> <b>116 (8)</b> 3204-3209
 *      </li>
 *  </ul>
 *
 *  <br><br>
 *  <ul>
 *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
 *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/README.md">Special Function Project</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/ode/README.md">Special Function Ordinary Differential Equations</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class KohlrauschPDFEstimate
{

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

        double[] tArray =
        {
             0.1,
             0.2,
             0.3,
             0.4,
             0.5,
             1.0,
             2.0,
             5.0,
            10.0,
        };
        double[] betaArray =
        {
             0.1,
             0.2,
             0.3,
             0.4,
             0.5,
             0.6,
             0.7,
             0.8,
             0.9,
        };
        double[] pValueArray =
        {
             0.05,
             0.10,
             0.15,
             0.20,
             0.25,
             0.30,
             0.35,
             0.40,
             0.45,
        };

        R1ToR1 gammaEstimator = new EulerIntegralSecondKind (null);

        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|                - Beta                                                                                                        ||");

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

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

        for (double beta : betaArray)
        {
            R1UnivariateScaledExponential r1UnivariateScaledExponential = new R1UnivariateScaledExponential (
                new ScaledExponentialEstimator (
                    beta,
                    1.
                ),
                gammaEstimator
            );

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

            for (double t : tArray)
            {
                display = display + " " + FormatUtil.FormatDouble (
                    r1UnivariateScaledExponential.density (t), 1, 8, 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|                - Beta                                                                                                        ||");

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

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

        for (double beta : betaArray)
        {
            R1UnivariateScaledExponential r1UnivariateScaledExponential = new R1UnivariateScaledExponential (
                new ScaledExponentialEstimator (
                    beta,
                    1.
                ),
                gammaEstimator
            );

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

            for (double t : tArray)
            {
                display = display + " " + FormatUtil.FormatDouble (
                    r1UnivariateScaledExponential.cumulative (t), 1, 8, 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|                - Beta                                                                                                        ||");

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

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

        for (double beta : betaArray)
        {
            R1UnivariateScaledExponential r1UnivariateScaledExponential = new R1UnivariateScaledExponential (
                new ScaledExponentialEstimator (
                    beta,
                    1.
                ),
                gammaEstimator
            );

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

            for (double p : pValueArray)
            {
                display = display + " " + FormatUtil.FormatDouble (
                    r1UnivariateScaledExponential.invCumulative (p), 1, 8, 1., false
                ) + " |";
            }

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

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

        EnvManager.TerminateEnv();
    }
}