R1CentralCLTProxy.java

  1. package org.drip.measure.chisquare;

  3. /*
  4.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  5.  */

  7. /*!
  8.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  9.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  10.  * 
  11.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  12.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  13.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  14.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  15.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  16.  *      and computational support.
  17.  *  
  18.  *      https://lakshmidrip.github.io/DROP/
  19.  *  
  20.  *  DROP is composed of three modules:
  21.  *  
  22.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  23.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  24.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  25.  * 
  26.  *  DROP Product Core implements libraries for the following:
  27.  *  - Fixed Income Analytics
  28.  *  - Loan Analytics
  29.  *  - Transaction Cost Analytics
  30.  * 
  31.  *  DROP Portfolio Core implements libraries for the following:
  32.  *  - Asset Allocation Analytics
  33.  *  - Asset Liability Management Analytics
  34.  *  - Capital Estimation Analytics
  35.  *  - Exposure Analytics
  36.  *  - Margin Analytics
  37.  *  - XVA Analytics
  38.  * 
  39.  *  DROP Computational Core implements libraries for the following:
  40.  *  - Algorithm Support
  41.  *  - Computation Support
  42.  *  - Function Analysis
  43.  *  - Model Validation
  44.  *  - Numerical Analysis
  45.  *  - Numerical Optimizer
  46.  *  - Spline Builder
  47.  *  - Statistical Learning
  48.  * 
  49.  *  Documentation for DROP is Spread Over:
  50.  * 
  51.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  52.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  53.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  54.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  55.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  56.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  57.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  58.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  59.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  60.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  61.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  62.  * 
  63.  *  Licensed under the Apache License, Version 2.0 (the "License");
  64.  *      you may not use this file except in compliance with the License.
  65.  *   
  66.  *  You may obtain a copy of the License at
  67.  *      http://www.apache.org/licenses/LICENSE-2.0
  68.  *  
  69.  *  Unless required by applicable law or agreed to in writing, software
  70.  *      distributed under the License is distributed on an "AS IS" BASIS,
  71.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  72.  *  
  73.  *  See the License for the specific language governing permissions and
  74.  *      limitations under the License.
  75.  */

  77. /**
  78.  * <i>R1CentralCLTProxy</i> implements the N (0, 1) CLT Proxy Version for the R<sup>1</sup> Chi-Square
  79.  *  Distribution. The References are:
  80.  * 
  81.  * <br><br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
  85.  *              on Mathematics</b>
  86.  *      </li>
  87.  *      <li>
  88.  *          Backstrom, T., and J. Fischer (2018): Fast Randomization for Distributed Low Bit-rate Coding of
  89.  *              Speech and Audio <i>IEEE/ACM Transactions on Audio, Speech, and Language Processing</i> <b>26
  90.  *              (1)</b> 19-30
  91.  *      </li>
  92.  *      <li>
  93.  *          Chi-Squared Distribution (2019): Chi-Squared Function
  94.  *              https://en.wikipedia.org/wiki/Chi-squared_distribution
  95.  *      </li>
  96.  *      <li>
  97.  *          Johnson, N. L., S. Kotz, and N. Balakrishnan (1994): <i>Continuous Univariate Distributions
  98.  *              2<sup>nd</sup> Edition</i> <b>John Wiley and Sons</b>
  99.  *      </li>
  100.  *      <li>
  101.  *          National Institute of Standards and Technology (2019): Chi-Squared Distribution
  102.  *              https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm
  103.  *      </li>
  104.  *  </ul>
  105.  *
  106.  *  <br><br>
  107.  *  <ul>
  108.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  109.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  110.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/README.md">R<sup>d</sup> Continuous/Discrete Probability Measures</a></li>
  111.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/chisquare/README.md">Chi-Square Distribution Implementation/Properties</a></li>
  112.  *  </ul>
  113.  *
  114.  * @author Lakshmi Krishnamurthy
  115.  */

  117. public class R1CentralCLTProxy extends org.drip.measure.continuous.R1Univariate
  118. {
  119.     private int _degreesOfFreedom = -1;

  121.     private org.drip.measure.gaussian.R1UnivariateNormal _r1UnivariateNormal =
  122.         org.drip.measure.gaussian.R1UnivariateNormal.Standard();

  124.     /**
  125.      * R1CentralCLTProxy Constructor
  126.      * 
  127.      * @param degreesOfFreedom Degrees of Freedom
  128.      * 
  129.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  130.      */

  132.     public R1CentralCLTProxy (
  133.         final int degreesOfFreedom)
  134.         throws java.lang.Exception
  135.     {
  136.         if (0 >= (_degreesOfFreedom = degreesOfFreedom))
  137.         {
  138.             throw new java.lang.Exception ("R1CentralCLTProxy Constructor => Invalid Inputs");
  139.         }
  140.     }

  142.     /**
  143.      * Retrieve the Degrees of Freedom
  144.      * 
  145.      * @return The Degrees of Freedom
  146.      */

  148.     public int degreesOfFreedom()
  149.     {
  150.         return _degreesOfFreedom;
  151.     }

  153.     @Override public double[] support()
  154.     {
  155.         return new double[]
  156.         {
  157.             -1. * java.lang.Math.sqrt (0.5 * _degreesOfFreedom),
  158.             java.lang.Double.POSITIVE_INFINITY
  159.         };
  160.     }

  162.     @Override public double density (
  163.         final double t)
  164.         throws java.lang.Exception
  165.     {
  166.         return _r1UnivariateNormal.density (t);
  167.     }

  169.     @Override public double cumulative (
  170.         final double t)
  171.         throws java.lang.Exception
  172.     {
  173.         return _r1UnivariateNormal.cumulative (t);
  174.     }

  176.     @Override public double mean()
  177.         throws java.lang.Exception
  178.     {
  179.         return 0.;
  180.     }

  182.     @Override public double median()
  183.         throws java.lang.Exception
  184.     {
  185.         return 0.;
  186.     }

  188.     @Override public double mode()
  189.         throws java.lang.Exception
  190.     {
  191.         return 0.;
  192.     }

  194.     @Override public double variance()
  195.         throws java.lang.Exception
  196.     {
  197.         return 1.;
  198.     }

  200.     @Override public double skewness()
  201.         throws java.lang.Exception
  202.     {
  203.         return java.lang.Math.sqrt (8. / _degreesOfFreedom);
  204.     }

  206.     @Override public double excessKurtosis()
  207.         throws java.lang.Exception
  208.     {
  209.         return 12. / _degreesOfFreedom;
  210.     }

  212.     @Override public double differentialEntropy()
  213.         throws java.lang.Exception
  214.     {
  215.         return _r1UnivariateNormal.differentialEntropy();
  216.     }

  218.     @Override public org.drip.function.definition.R1ToR1 momentGeneratingFunction()
  219.     {
  220.         return _r1UnivariateNormal.momentGeneratingFunction();
  221.     }

  223.     @Override public org.drip.function.definition.R1ToR1 probabilityGeneratingFunction()
  224.     {
  225.         return _r1UnivariateNormal.probabilityGeneratingFunction();
  226.     }

  228.     @Override public double random()
  229.         throws java.lang.Exception
  230.     {
  231.         double sumOfStandardNormalSquares = 0.;

  233.         for (int drawIndex = 0; drawIndex < _degreesOfFreedom; ++drawIndex)
  234.         {
  235.             double randomStandardNormal = org.drip.measure.gaussian.NormalQuadrature.InverseCDF
  236.                 (java.lang.Math.random());

  238.             sumOfStandardNormalSquares = sumOfStandardNormalSquares +
  239.                 randomStandardNormal * randomStandardNormal;
  240.         }

  242.         return (sumOfStandardNormalSquares - _degreesOfFreedom) /
  243.             java.lang.Math.sqrt (2. * _degreesOfFreedom);
  244.     }
  245. }
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