ProbabilityIntegralTransform.java

  1. package org.drip.validation.hypothesis;

  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>ProbabilityIntegralTransform</i> holds the PIT Distribution CDF of the Test-Statistic Response over the
  79.  * Outcome Instances.
  80.  *
  81.  *  <br><br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Bhattacharya, B., and D. Habtzghi (2002): Median of the p-value under the Alternate Hypothesis
  85.  *              American Statistician 56 (3) 202-206
  86.  *      </li>
  87.  *      <li>
  88.  *          Head, M. L., L. Holman, R, Lanfear, A. T. Kahn, and M. D. Jennions (2015): The Extent and
  89.  *              Consequences of p-Hacking in Science PLoS Biology 13 (3) e1002106
  90.  *      </li>
  91.  *      <li>
  92.  *          Wasserstein, R. L., and N. A. Lazar (2016): The ASA’s Statement on p-values: Context, Process,
  93.  *              and Purpose American Statistician 70 (2) 129-133
  94.  *      </li>
  95.  *      <li>
  96.  *          Wikipedia (2018): Probability Integral Transform
  97.  *              https://en.wikipedia.org/wiki/Probability_integral_transform
  98.  *      </li>
  99.  *      <li>
  100.  *          Wikipedia (2019): p-value https://en.wikipedia.org/wiki/P-value
  101.  *      </li>
  102.  *  </ul>
  103.  *
  104.  *  <br><br>
  105.  *  <ul>
  106.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  107.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ModelValidationAnalyticsLibrary.md">Model Validation Analytics Library</a></li>
  108.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/validation/README.md">Risk Factor and Hypothesis Validation, Evidence Processing, and Model Testing</a></li>
  109.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/validation/hypothesis/README.md">Statistical Hypothesis Validation Test Suite</a></li>
  110.  *  </ul>
  111.  * <br><br>
  112.  *
  113.  * @author Lakshmi Krishnamurthy
  114.  */

  116. public class ProbabilityIntegralTransform
  117. {
  118.     private java.util.Map<java.lang.Double, java.lang.Double> _pValueTestStatisticMap = null;
  119.     private java.util.Map<java.lang.Double, java.lang.Double> _testStatisticPValueMap = null;

  121.     /**
  122.      * ProbabilityIntegralTransform Constructor
  123.      * 
  124.      * @param testStatisticPValueMap Test Statistic - p Value Map
  125.      * 
  126.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  127.      */

  129.     public ProbabilityIntegralTransform (
  130.         final java.util.Map<java.lang.Double, java.lang.Double> testStatisticPValueMap)
  131.         throws java.lang.Exception
  132.     {
  133.         if (null == (_testStatisticPValueMap = testStatisticPValueMap) ||
  134.             0 == _testStatisticPValueMap.size())
  135.         {
  136.             throw new java.lang.Exception ("ProbabilityIntegralTransform Constructor => Invalid Inputs");
  137.         }

  139.         _pValueTestStatisticMap = new java.util.TreeMap<java.lang.Double, java.lang.Double>();

  141.         for (java.util.Map.Entry<java.lang.Double, java.lang.Double> testStatisticPValueMapEntry :
  142.             _testStatisticPValueMap.entrySet())
  143.         {
  144.             _pValueTestStatisticMap.put (
  145.                 testStatisticPValueMapEntry.getValue(),
  146.                 testStatisticPValueMapEntry.getKey()
  147.             );
  148.         }
  149.     }

  151.     /**
  152.      * Retrieve the p Value - Test Statistic Map
  153.      * 
  154.      * @return The p Value - Test Statistic Map
  155.      */

  157.     public java.util.Map<java.lang.Double, java.lang.Double> pValueTestStatisticMap()
  158.     {
  159.         return _pValueTestStatisticMap;
  160.     }

  162.     /**
  163.      * Retrieve the Test Statistic - p Value Map
  164.      * 
  165.      * @return The Test Statistic - p Value Map
  166.      */

  168.     public java.util.Map<java.lang.Double, java.lang.Double> testStatisticPValueMap()
  169.     {
  170.         return _testStatisticPValueMap;
  171.     }

  173.     /**
  174.      * Compute the p-Value corresponding to the Test Statistic Instance
  175.      * 
  176.      * @param testStatistic The Test Statistic Instance
  177.      * 
  178.      * @return The p-Value
  179.      * 
  180.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  181.      */

  183.     public double pValue (
  184.         final double testStatistic)
  185.         throws java.lang.Exception
  186.     {
  187.         if (!org.drip.numerical.common.NumberUtil.IsValid (testStatistic))
  188.         {
  189.             throw new java.lang.Exception ("ProbabilityIntegralTransform::pValue => Invalid Inputs");
  190.         }

  192.         java.util.Set<java.lang.Double> testStatisticKeySet = _testStatisticPValueMap.keySet();

  194.         double testStatisticKeyCurrent = java.lang.Double.NaN;
  195.         double testStatisticKeyPrevious = java.lang.Double.NaN;

  197.         for (double testStatisticKey : testStatisticKeySet)
  198.         {
  199.             if (testStatistic == testStatisticKey)
  200.             {
  201.                 return _testStatisticPValueMap.get (testStatistic);
  202.             }

  204.             if (testStatistic < testStatisticKey)
  205.             {
  206.                 if (!org.drip.numerical.common.NumberUtil.IsValid (testStatisticKeyPrevious))
  207.                 {
  208.                     return 0.;
  209.                 }

  211.                 testStatisticKeyCurrent = testStatisticKey;
  212.                 break;
  213.             }

  215.             testStatisticKeyPrevious = testStatisticKey;
  216.         }

  218.         return !org.drip.numerical.common.NumberUtil.IsValid (testStatisticKeyCurrent) ||
  219.             testStatistic >= testStatisticKeyCurrent ? 1. :
  220.             ((testStatistic - testStatisticKeyPrevious) * _testStatisticPValueMap.get
  221.                 (testStatisticKeyCurrent) +
  222.             (testStatisticKeyCurrent - testStatistic) * _testStatisticPValueMap.get
  223.                 (testStatisticKeyPrevious)) /
  224.             (testStatisticKeyCurrent - testStatisticKeyPrevious);
  225.     }

  227.     /**
  228.      * Compute the Test Statistic Instance corresponding to the p-Value
  229.      * 
  230.      * @param pValue The p-Value
  231.      * 
  232.      * @return The Response Instance
  233.      * 
  234.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  235.      */

  237.     public double testStatistic (
  238.         final double pValue)
  239.         throws java.lang.Exception
  240.     {
  241.         if (!org.drip.numerical.common.NumberUtil.IsValid (pValue))
  242.         {
  243.             throw new java.lang.Exception ("ProbabilityIntegralTransform::testStatistic => Invalid Inputs");
  244.         }

  246.         java.util.Set<java.lang.Double> pValueKeySet = _pValueTestStatisticMap.keySet();

  248.         double pValueKeyCurrent = java.lang.Double.NaN;
  249.         double pValueKeyPrevious = java.lang.Double.NaN;

  251.         for (double pValueKey : pValueKeySet)
  252.         {
  253.             if (pValue == pValueKey)
  254.             {
  255.                 return _pValueTestStatisticMap.get (pValue);
  256.             }

  258.             if (pValue < pValueKey)
  259.             {
  260.                 if (!org.drip.numerical.common.NumberUtil.IsValid (pValueKeyPrevious))
  261.                 {
  262.                     return _pValueTestStatisticMap.get (pValueKey);
  263.                 }

  265.                 pValueKeyCurrent = pValueKey;
  266.                 break;
  267.             }

  269.             pValueKeyPrevious = pValueKey;
  270.         }

  272.         return pValue >= pValueKeyCurrent ? _pValueTestStatisticMap.get (pValueKeyCurrent) :
  273.             ((pValue - pValueKeyPrevious) * _pValueTestStatisticMap.get (pValueKeyCurrent) +
  274.             (pValueKeyCurrent - pValue) * _pValueTestStatisticMap.get (pValueKeyPrevious)) /
  275.             (pValueKeyCurrent - pValueKeyPrevious);
  276.     }
  277. }
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