StretchedExponentialMomentEstimate.java

  1. package org.drip.sample.gamma;

  3. import org.drip.numerical.common.FormatUtil;
  4. import org.drip.service.env.EnvManager;
  5. import org.drip.specialfunction.derived.StretchedExponentialMoment;

  7. /*
  8.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  9.  */

  11. /*!
  12.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  13.  * 
  14.  *  This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
  15.  *      calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
  16.  *      FX, and structured products.
  17.  *  
  18.  *      https://lakshmidrip.github.io/DROP/
  19.  *  
  20.  *  DROP is composed of three main modules:
  21.  *  
  22.  *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
  23.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  24.  *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
  25.  * 
  26.  *  DROP Analytics Core implements libraries for the following:
  27.  *  - Fixed Income Analytics
  28.  *  - Asset Backed Analytics
  29.  *  - XVA Analytics
  30.  *  - Exposure and Margin Analytics
  31.  * 
  32.  *  DROP Portfolio Core implements libraries for the following:
  33.  *  - Asset Allocation Analytics
  34.  *  - Transaction Cost Analytics
  35.  * 
  36.  *  DROP Numerical Core implements libraries for the following:
  37.  *  - Statistical Learning Library
  38.  *  - Numerical Optimizer Library
  39.  *  - Machine Learning Library
  40.  *  - Spline Builder Library
  41.  * 
  42.  *  Documentation for DROP is Spread Over:
  43.  * 
  44.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  45.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  46.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  47.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  48.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  49.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  50.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  51.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  52.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  53.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  54.  * 
  55.  *  Licensed under the Apache License, Version 2.0 (the "License");
  56.  *      you may not use this file except in compliance with the License.
  57.  *   
  58.  *  You may obtain a copy of the License at
  59.  *      http://www.apache.org/licenses/LICENSE-2.0
  60.  *  
  61.  *  Unless required by applicable law or agreed to in writing, software
  62.  *      distributed under the License is distributed on an "AS IS" BASIS,
  63.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  64.  *  
  65.  *  See the License for the specific language governing permissions and
  66.  *      limitations under the License.
  67.  */

  69. /**
  70.  * <i>StretchedExponentialMomentEstimate</i> demonstrates the Estimation of the Moments of the Stretched
  71.  * Exponential Function. The References are:
  72.  * 
  73.  * <br><br>
  74.  *  <ul>
  75.  *      <li>
  76.  *          Blagouchine, I. V. (2014): Re-discovery of Malmsten's Integrals, their Evaluation by Contour
  77.  *              Integration Methods, and some Related Results <i>Ramanujan Journal</i> <b>35 (1)</b> 21-110
  78.  *      </li>
  79.  *      <li>
  80.  *          Borwein, J. M., and R. M. Corless (2017): Gamma Function and the Factorial in the Monthly
  81.  *              https://arxiv.org/abs/1703.05349 <b>arXiv</b>
  82.  *      </li>
  83.  *      <li>
  84.  *          Davis, P. J. (1959): Leonhard Euler's Integral: A Historical Profile of the Gamma Function
  85.  *              <i>American Mathematical Monthly</i> <b>66 (10)</b> 849-869
  86.  *      </li>
  87.  *      <li>
  88.  *          Whitaker, E. T., and G. N. Watson (1996): <i>A Course on Modern Analysis</i> <b>Cambridge
  89.  *              University Press</b> New York
  90.  *      </li>
  91.  *      <li>
  92.  *          Wikipedia (2019): Gamma Function https://en.wikipedia.org/wiki/Gamma_function
  93.  *      </li>
  94.  *  </ul>
  95.  *
  96.  *  <br><br>
  97.  *  <ul>
  98.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
  99.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalOptimizerLibrary.md">Numerical Optimizer</a></li>
  100.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">Function</a></li>
  101.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/gamma/README.md">Integrand Estimates of Gamma Functions</a></li>
  102.  *  </ul>
  103.  *
  104.  * @author Lakshmi Krishnamurthy
  105.  */

  107. public class StretchedExponentialMomentEstimate
  108. {

  110.     private static final void Estimate (
  111.         final double tau,
  112.         final double beta,
  113.         final double[] momentArray)
  114.         throws Exception
  115.     {
  116.         StretchedExponentialMoment stretchedExponentialMomentIntegral = new StretchedExponentialMoment (
  117.             null,
  118.             tau,
  119.             beta
  120.         );

  122.         StretchedExponentialMoment stretchedExponentialMomentWeierstrass =
  123.             StretchedExponentialMoment.Weierstrass (
  124.                 tau,
  125.                 beta,
  126.                 1638400
  127.             );

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

  132.         for (double moment : momentArray)
  133.         {
  134.             display = display + "{" + FormatUtil.FormatDouble (
  135.                 stretchedExponentialMomentIntegral.evaluate (moment), 7, 2, 1.
  136.             ) + " |" + FormatUtil.FormatDouble (
  137.                 stretchedExponentialMomentWeierstrass.evaluate (moment), 7, 2, 1.
  138.             ) + "}";
  139.         }

  141.         System.out.println (display + "|");
  142.     }

  144.     public static final void main (
  145.         final String[] argumentArray)
  146.         throws Exception
  147.     {
  148.         EnvManager.InitEnv ("");

  150.         double[] tauArray =
  151.         {
  152.             0.5,
  153.             1.0,
  154.             1.5,
  155.             2.0,
  156.         };
  157.         double[] betaArray =
  158.         {
  159.             0.5,
  160.             1.0,
  161.             1.5,
  162.             2.0,
  163.         };
  164.         double[] momentArray =
  165.         {
  166.             1.,
  167.             2.,
  168.             3.,
  169.             4.,
  170.             5.,
  171.         };

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

  176.         System.out.println
  177.             ("\t|                                             STRETCHED EXPONENTIAL INTEGRAL vs. WERERSTRASS ESTIMATE                                             |");

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

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

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

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

  191.         System.out.println
  192.             ("\t|                - Integral vs. Weierstrass Moment Comparison                                                                                     |");

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

  197.         for (double tau : tauArray)
  198.         {
  199.             for (double beta : betaArray)
  200.             {
  201.                 Estimate (
  202.                     tau,
  203.                     beta,
  204.                     momentArray
  205.                 );
  206.             }
  207.         }

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

  212.         EnvManager.TerminateEnv();
  213.     }
  214. }
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