CumulativeBinomialDistribution.java

  1. package org.drip.sample.beta;

  3. import org.drip.numerical.common.FormatUtil;
  4. import org.drip.service.env.EnvManager;
  5. import org.drip.specialfunction.beta.CombinatorialEstimate;
  6. import org.drip.specialfunction.beta.IncompleteIntegrandEstimator;
  7. import org.drip.specialfunction.beta.IncompleteRegularizedEstimator;
  8. import org.drip.specialfunction.beta.IntegrandEstimator;

  10. /*
  11.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  12.  */

  14. /*!
  15.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  16.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  17.  * 
  18.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  19.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  20.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  21.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  22.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  23.  *      and computational support.
  24.  *  
  25.  *      https://lakshmidrip.github.io/DROP/
  26.  *  
  27.  *  DROP is composed of three modules:
  28.  *  
  29.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  30.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  31.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  32.  * 
  33.  *  DROP Product Core implements libraries for the following:
  34.  *  - Fixed Income Analytics
  35.  *  - Loan Analytics
  36.  *  - Transaction Cost Analytics
  37.  * 
  38.  *  DROP Portfolio Core implements libraries for the following:
  39.  *  - Asset Allocation Analytics
  40.  *  - Asset Liability Management Analytics
  41.  *  - Capital Estimation Analytics
  42.  *  - Exposure Analytics
  43.  *  - Margin Analytics
  44.  *  - XVA Analytics
  45.  * 
  46.  *  DROP Computational Core implements libraries for the following:
  47.  *  - Algorithm Support
  48.  *  - Computation Support
  49.  *  - Function Analysis
  50.  *  - Model Validation
  51.  *  - Numerical Analysis
  52.  *  - Numerical Optimizer
  53.  *  - Spline Builder
  54.  *  - Statistical Learning
  55.  * 
  56.  *  Documentation for DROP is Spread Over:
  57.  * 
  58.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  59.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  60.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  61.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  62.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  63.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  64.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  65.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  66.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  67.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  68.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  69.  * 
  70.  *  Licensed under the Apache License, Version 2.0 (the "License");
  71.  *      you may not use this file except in compliance with the License.
  72.  *   
  73.  *  You may obtain a copy of the License at
  74.  *      http://www.apache.org/licenses/LICENSE-2.0
  75.  *  
  76.  *  Unless required by applicable law or agreed to in writing, software
  77.  *      distributed under the License is distributed on an "AS IS" BASIS,
  78.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  79.  *  
  80.  *  See the License for the specific language governing permissions and
  81.  *      limitations under the License.
  82.  */

  84. /**
  85.  * <i>CumulativeBinomialDistribution</i> illustrates the Computation of the Cumulative Binomial Distribution
  86.  * Values using the Incomplete Beta Function. The References are:
  87.  * 
  88.  * <br><br>
  89.  *  <ul>
  90.  *      <li>
  91.  *          Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
  92.  *              on Mathematics</b>
  93.  *      </li>
  94.  *      <li>
  95.  *          Davis, P. J. (1959): Leonhard Euler's Integral: A Historical Profile of the Gamma Function
  96.  *              <i>American Mathematical Monthly</i> <b>66 (10)</b> 849-869
  97.  *      </li>
  98.  *      <li>
  99.  *          Whitaker, E. T., and G. N. Watson (1996): <i>A Course on Modern Analysis</i> <b>Cambridge
  100.  *              University Press</b> New York
  101.  *      </li>
  102.  *      <li>
  103.  *          Wikipedia (2019): Beta Function https://en.wikipedia.org/wiki/Beta_function
  104.  *      </li>
  105.  *      <li>
  106.  *          Wikipedia (2019): Gamma Function https://en.wikipedia.org/wiki/Gamma_function
  107.  *      </li>
  108.  *  </ul>
  109.  *
  110.  *  <br><br>
  111.  *  <ul>
  112.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  113.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
  114.  *      <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>
  115.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/beta/README.md">Estimates of the Beta Functions</a></li>
  116.  *  </ul>
  117.  *
  118.  * @author Lakshmi Krishnamurthy
  119.  */

  121. public class CumulativeBinomialDistribution
  122. {

  124.     private static final void Estimate (
  125.         final double[] pArray,
  126.         final double n,
  127.         final double k,
  128.         final IncompleteRegularizedEstimator incompleteRegularizedEstimator)
  129.         throws Exception
  130.     {
  131.         String display =
  132.             "\t| {n:" +
  133.             FormatUtil.FormatDouble (n, 2, 0, 1., false) + ", k:" +
  134.             FormatUtil.FormatDouble (k, 2, 0, 1., false) + "} =>";

  136.         for (double p : pArray)
  137.         {
  138.             display = display + FormatUtil.FormatDouble (
  139.                 CombinatorialEstimate.CumulativeBinomialDistribution (
  140.                     n,
  141.                     k,
  142.                     p,
  143.                     incompleteRegularizedEstimator
  144.                 ), 1, 8, 1.
  145.             ) + " |";
  146.         }

  148.         System.out.println (display + "|");
  149.     }

  151.     public static final void main (
  152.         final String[] argumentArray)
  153.         throws Exception
  154.     {
  155.         EnvManager.InitEnv ("");

  157.         double[] pArray =
  158.         {
  159.             1.00,
  160.             0.80,
  161.             0.60,
  162.             0.40,
  163.             0.20,
  164.             0.00,
  165.         };
  166.         double[] nArray =
  167.         {
  168.             99,
  169.         };
  170.         double[] kArray =
  171.         {
  172.              5,
  173.             10,
  174.             15,
  175.             20,
  176.             25,
  177.             30,
  178.             35,
  179.             40,
  180.             45,
  181.             50,
  182.             55,
  183.             60,
  184.             65,
  185.             70,
  186.             75,
  187.             80,
  188.             85,
  189.             90,
  190.             95,
  191.         };

  193.         int eulerIntegrandBetaTermCount = 1000;
  194.         int eulerIntegrandIncompleteBetaTermCount = 1000;

  196.         IncompleteRegularizedEstimator incompleteRegularizedEstimator = new IncompleteRegularizedEstimator (
  197.             IncompleteIntegrandEstimator.EulerFirst (eulerIntegrandIncompleteBetaTermCount),
  198.             IntegrandEstimator.EulerFirstRightPlane (eulerIntegrandBetaTermCount)
  199.         );

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

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

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

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

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

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

  213.         System.out.println ("\t|                - Cumulative Binomial Distribution Estimate                                  ||");

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

  217.         for (double n : nArray)
  218.         {
  219.             for (double k : kArray)
  220.             {
  221.                 Estimate (
  222.                     pArray,
  223.                     n,
  224.                     k,
  225.                     incompleteRegularizedEstimator
  226.                 );
  227.             }
  228.         }

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

  232.         EnvManager.TerminateEnv();
  233.     }
  234. }
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