CentralChernoffBounds.java

  1. package org.drip.sample.chisquaredistribution;

  3. import org.drip.function.definition.R1ToR1;
  4. import org.drip.function.definition.R2ToR1;
  5. import org.drip.measure.chisquare.R1Central;
  6. import org.drip.numerical.common.FormatUtil;
  7. import org.drip.service.env.EnvManager;
  8. import org.drip.specialfunction.digamma.CumulativeSeriesEstimator;
  9. import org.drip.specialfunction.gamma.EulerIntegralSecondKind;
  10. import org.drip.specialfunction.incompletegamma.LowerEulerIntegral;

  12. /*
  13.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  14.  */

  16. /*!
  17.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  18.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  19.  * 
  20.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  21.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  22.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  23.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  24.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  25.  *      and computational support.
  26.  *  
  27.  *      https://lakshmidrip.github.io/DROP/
  28.  *  
  29.  *  DROP is composed of three modules:
  30.  *  
  31.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  32.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  33.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  34.  * 
  35.  *  DROP Product Core implements libraries for the following:
  36.  *  - Fixed Income Analytics
  37.  *  - Loan Analytics
  38.  *  - Transaction Cost Analytics
  39.  * 
  40.  *  DROP Portfolio Core implements libraries for the following:
  41.  *  - Asset Allocation Analytics
  42.  *  - Asset Liability Management Analytics
  43.  *  - Capital Estimation Analytics
  44.  *  - Exposure Analytics
  45.  *  - Margin Analytics
  46.  *  - XVA Analytics
  47.  * 
  48.  *  DROP Computational Core implements libraries for the following:
  49.  *  - Algorithm Support
  50.  *  - Computation Support
  51.  *  - Function Analysis
  52.  *  - Model Validation
  53.  *  - Numerical Analysis
  54.  *  - Numerical Optimizer
  55.  *  - Spline Builder
  56.  *  - Statistical Learning
  57.  * 
  58.  *  Documentation for DROP is Spread Over:
  59.  * 
  60.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  61.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  62.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  63.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  64.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  65.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  66.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  67.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  68.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  69.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  70.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  71.  * 
  72.  *  Licensed under the Apache License, Version 2.0 (the "License");
  73.  *      you may not use this file except in compliance with the License.
  74.  *   
  75.  *  You may obtain a copy of the License at
  76.  *      http://www.apache.org/licenses/LICENSE-2.0
  77.  *  
  78.  *  Unless required by applicable law or agreed to in writing, software
  79.  *      distributed under the License is distributed on an "AS IS" BASIS,
  80.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  81.  *  
  82.  *  See the License for the specific language governing permissions and
  83.  *      limitations under the License.
  84.  */

  86. /**
  87.  * <i>CentralChernoffBounds</i> illustrates the Upper Chernoff Bounds for the Central Chi-squared Function.
  88.  * The References are:
  89.  * 
  90.  * <br><br>
  91.  *  <ul>
  92.  *      <li>
  93.  *          Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
  94.  *              on Mathematics</b>
  95.  *      </li>
  96.  *      <li>
  97.  *          Backstrom, T., and J. Fischer (2018): Fast Randomization for Distributed Low Bit-rate Coding of
  98.  *              Speech and Audio <i>IEEE/ACM Transactions on Audio, Speech, and Language Processing</i> <b>26
  99.  *              (1)</b> 19-30
  100.  *      </li>
  101.  *      <li>
  102.  *          Chi-Squared Distribution (2019): Chi-Squared Function
  103.  *              https://en.wikipedia.org/wiki/Chi-squared_distribution
  104.  *      </li>
  105.  *      <li>
  106.  *          Johnson, N. L., S. Kotz, and N. Balakrishnan (1994): <i>Continuous Univariate Distributions
  107.  *              2<sup>nd</sup> Edition</i> <b>John Wiley and Sons</b>
  108.  *      </li>
  109.  *      <li>
  110.  *          National Institute of Standards and Technology (2019): Chi-Squared Distribution
  111.  *              https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm
  112.  *      </li>
  113.  *  </ul>
  114.  *
  115.  *  <br><br>
  116.  *  <ul>
  117.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  118.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  119.  *      <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>
  120.  *      <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>
  121.  *  </ul>
  122.  *
  123.  * @author Lakshmi Krishnamurthy
  124.  */

  126. public class CentralChernoffBounds
  127. {

  129.     private static final R2ToR1 LowerIncompleteGamma()
  130.         throws Exception
  131.     {
  132.         return new R2ToR1()
  133.         {
  134.             @Override public double evaluate (
  135.                 final double s,
  136.                 final double t)
  137.                 throws Exception
  138.             {
  139.                 return new LowerEulerIntegral (
  140.                     null,
  141.                     t
  142.                 ).evaluate (s);
  143.             }
  144.         };
  145.     }

  147.     public static final void main (
  148.         final String[] argumentArray)
  149.         throws Exception
  150.     {
  151.         EnvManager.InitEnv ("");

  153.         int digammaTermCount = 1000;
  154.         double[] zArray =
  155.         {
  156.              0.01,
  157.              0.03,
  158.              0.06,
  159.              0.10,
  160.              0.30,
  161.              0.60,
  162.              0.99,
  163.              3.00,
  164.              6.00,
  165.             10.00,
  166.         };
  167.         int[] dofArray =
  168.         {
  169.              // 1,
  170.              2,
  171.              3,
  172.              4,
  173.              5,
  174.              6,
  175.              7,
  176.              8,
  177.              9,
  178.         };

  180.         R1ToR1 gammaEstimator = new EulerIntegralSecondKind (null);

  182.         R2ToR1 lowerIncompleteGammaEstimator = LowerIncompleteGamma();

  184.         R1ToR1 digammaEstimator = CumulativeSeriesEstimator.AbramowitzStegun2007 (digammaTermCount);

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

  188.         System.out.println ("\t|                                           CUMULATIVE DISTRIBUTION FUNCTION ESTIMATE                                          ||");

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

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

  194.         System.out.println ("\t|                - Degrees of Freedom                                                                                          ||");

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

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

  200.         for (int dof : dofArray)
  201.         {
  202.             R1Central r1Univariate = new R1Central (
  203.                 dof,
  204.                 gammaEstimator,
  205.                 digammaEstimator,
  206.                 lowerIncompleteGammaEstimator
  207.             );

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

  211.             for (double z : zArray)
  212.             {
  213.                 display = display + " " + FormatUtil.FormatDouble (
  214.                     r1Univariate.cumulative (z * dof), 1, 5, 1., false
  215.                 ) + " |";
  216.             }

  218.             System.out.println (display + "|");
  219.         }

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

  223.         System.out.println();

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

  227.         System.out.println ("\t|                                        CUMULATIVE DISTRIBUTION CHERNOFF BOUND ESTIMATE                                       ||");

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

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

  233.         System.out.println ("\t|                - Degrees of Freedom                                                                                          ||");

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

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

  239.         for (int dof : dofArray)
  240.         {
  241.             R1Central r1Univariate = new R1Central (
  242.                 dof,
  243.                 gammaEstimator,
  244.                 digammaEstimator,
  245.                 lowerIncompleteGammaEstimator
  246.             );

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

  250.             for (double z : zArray)
  251.             {
  252.                 display = display + " " + FormatUtil.FormatDouble (
  253.                     r1Univariate.chernoffBound (z * dof), 1, 5, 1., false
  254.                 ) + " |";
  255.             }

  257.             System.out.println (display + "|");
  258.         }

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

  262.         System.out.println();

  264.         EnvManager.TerminateEnv();
  265.     }
  266. }
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