CumulativeBinomialDistributionProperty.java

  1. package org.drip.sample.beta;

  3. import org.drip.function.definition.R1PropertyVerification;
  4. import org.drip.numerical.common.FormatUtil;
  5. import org.drip.service.env.EnvManager;
  6. import org.drip.specialfunction.property.IncompleteBetaEqualityLemma;

  8. /*
  9.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  10.  */

  12. /*!
  13.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  14.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  15.  * 
  16.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  17.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  18.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  19.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  20.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  21.  *      and computational support.
  22.  *  
  23.  *      https://lakshmidrip.github.io/DROP/
  24.  *  
  25.  *  DROP is composed of three modules:
  26.  *  
  27.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  28.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  29.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  30.  * 
  31.  *  DROP Product Core implements libraries for the following:
  32.  *  - Fixed Income Analytics
  33.  *  - Loan Analytics
  34.  *  - Transaction Cost Analytics
  35.  * 
  36.  *  DROP Portfolio Core implements libraries for the following:
  37.  *  - Asset Allocation Analytics
  38.  *  - Asset Liability Management Analytics
  39.  *  - Capital Estimation Analytics
  40.  *  - Exposure Analytics
  41.  *  - Margin Analytics
  42.  *  - XVA Analytics
  43.  * 
  44.  *  DROP Computational Core implements libraries for the following:
  45.  *  - Algorithm Support
  46.  *  - Computation Support
  47.  *  - Function Analysis
  48.  *  - Model Validation
  49.  *  - Numerical Analysis
  50.  *  - Numerical Optimizer
  51.  *  - Spline Builder
  52.  *  - Statistical Learning
  53.  * 
  54.  *  Documentation for DROP is Spread Over:
  55.  * 
  56.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  57.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  58.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  59.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  60.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  61.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  62.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  63.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  64.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  65.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  66.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  67.  * 
  68.  *  Licensed under the Apache License, Version 2.0 (the "License");
  69.  *      you may not use this file except in compliance with the License.
  70.  *   
  71.  *  You may obtain a copy of the License at
  72.  *      http://www.apache.org/licenses/LICENSE-2.0
  73.  *  
  74.  *  Unless required by applicable law or agreed to in writing, software
  75.  *      distributed under the License is distributed on an "AS IS" BASIS,
  76.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  77.  *  
  78.  *  See the License for the specific language governing permissions and
  79.  *      limitations under the License.
  80.  */

  82. /**
  83.  * <i>CumulativeBinomialDistributionProperty</i> illustrates the Verification of the Cumulative Binomial
  84.  * Distribution Property. The References are:
  85.  * 
  86.  * <br><br>
  87.  *  <ul>
  88.  *      <li>
  89.  *          Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
  90.  *              on Mathematics</b>
  91.  *      </li>
  92.  *      <li>
  93.  *          Davis, P. J. (1959): Leonhard Euler's Integral: A Historical Profile of the Gamma Function
  94.  *              <i>American Mathematical Monthly</i> <b>66 (10)</b> 849-869
  95.  *      </li>
  96.  *      <li>
  97.  *          Whitaker, E. T., and G. N. Watson (1996): <i>A Course on Modern Analysis</i> <b>Cambridge
  98.  *              University Press</b> New York
  99.  *      </li>
  100.  *      <li>
  101.  *          Wikipedia (2019): Beta Function https://en.wikipedia.org/wiki/Beta_function
  102.  *      </li>
  103.  *      <li>
  104.  *          Wikipedia (2019): Gamma Function https://en.wikipedia.org/wiki/Gamma_function
  105.  *      </li>
  106.  *  </ul>
  107.  *
  108.  *  <br><br>
  109.  *  <ul>
  110.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  111.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
  112.  *      <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>
  113.  *      <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>
  114.  *  </ul>
  115.  *
  116.  * @author Lakshmi Krishnamurthy
  117.  */

  119. public class CumulativeBinomialDistributionProperty
  120. {

  122.     private static final void Verifier (
  123.         final double p,
  124.         final double n,
  125.         final double k)
  126.         throws Exception
  127.     {
  128.         R1PropertyVerification verification =
  129.             IncompleteBetaEqualityLemma.CumulativeBinomialDistribution().verify (
  130.                 p,
  131.                 n,
  132.                 k
  133.             );

  135.         System.out.println (
  136.             "\t| {p=" + FormatUtil.FormatDouble (p, 1, 2, 1., false) + "; n=" +
  137.             FormatUtil.FormatDouble (n, 2, 0, 1., false) + ", k=" +
  138.             FormatUtil.FormatDouble (k, 2, 0, 1., false) + "} => " +
  139.             FormatUtil.FormatDouble (verification.lValue(), 1, 10, 1.) + " | " +
  140.             FormatUtil.FormatDouble (verification.rValue(), 1, 10, 1.) + " | " +
  141.             verification.verified() + " ||"
  142.         );
  143.     }

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

  151.         double[] pArray =
  152.         {
  153.             1.00,
  154.             0.80,
  155.             0.60,
  156.             0.40,
  157.             0.20,
  158.         };
  159.         double[] nArray =
  160.         {
  161.             99,
  162.         };
  163.         double[] kArray =
  164.         {
  165.              5,
  166.             10,
  167.             15,
  168.             20,
  169.             25,
  170.             30,
  171.             35,
  172.             40,
  173.             45,
  174.             50,
  175.             55,
  176.             60,
  177.             65,
  178.             70,
  179.             75,
  180.             80,
  181.             85,
  182.             90,
  183.             95,
  184.         };

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

  188.         System.out.println ("\t|           CUMULATIVE BINOMIAL DISTRIBUTION PROPERTY          ||");

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

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

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

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

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

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

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

  204.         System.out.println ("\t|                - Verification Success?                       ||");

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

  208.         for (double p : pArray)
  209.         {
  210.             for (double n : nArray)
  211.             {
  212.                 for (double k : kArray)
  213.                 {
  214.                     Verifier (
  215.                         p,
  216.                         n,
  217.                         k
  218.                     );
  219.                 }
  220.             }
  221.         }

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

  225.         EnvManager.TerminateEnv();
  226.     }
  227. }
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