ProbabilityIntegralTransform.java
package org.drip.validation.hypothesis;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
* asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
* analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
* equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
* numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
* and computational support.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
*
* DROP Product Core implements libraries for the following:
* - Fixed Income Analytics
* - Loan Analytics
* - Transaction Cost Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Asset Liability Management Analytics
* - Capital Estimation Analytics
* - Exposure Analytics
* - Margin Analytics
* - XVA Analytics
*
* DROP Computational Core implements libraries for the following:
* - Algorithm Support
* - Computation Support
* - Function Analysis
* - Model Validation
* - Numerical Analysis
* - Numerical Optimizer
* - Spline Builder
* - Statistical Learning
*
* Documentation for DROP is Spread Over:
*
* - Main => https://lakshmidrip.github.io/DROP/
* - Wiki => https://github.com/lakshmiDRIP/DROP/wiki
* - GitHub => https://github.com/lakshmiDRIP/DROP
* - Repo Layout Taxonomy => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
* - Javadoc => https://lakshmidrip.github.io/DROP/Javadoc/index.html
* - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
* - Release Versions => https://lakshmidrip.github.io/DROP/version.html
* - Community Credits => https://lakshmidrip.github.io/DROP/credits.html
* - Issues Catalog => https://github.com/lakshmiDRIP/DROP/issues
* - JUnit => https://lakshmidrip.github.io/DROP/junit/index.html
* - Jacoco => https://lakshmidrip.github.io/DROP/jacoco/index.html
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
*
* You may obtain a copy of the License at
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
*
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/**
* <i>ProbabilityIntegralTransform</i> holds the PIT Distribution CDF of the Test-Statistic Response over the
* Outcome Instances.
*
* <br><br>
* <ul>
* <li>
* Bhattacharya, B., and D. Habtzghi (2002): Median of the p-value under the Alternate Hypothesis
* American Statistician 56 (3) 202-206
* </li>
* <li>
* Head, M. L., L. Holman, R, Lanfear, A. T. Kahn, and M. D. Jennions (2015): The Extent and
* Consequences of p-Hacking in Science PLoS Biology 13 (3) e1002106
* </li>
* <li>
* Wasserstein, R. L., and N. A. Lazar (2016): The ASA’s Statement on p-values: Context, Process,
* and Purpose American Statistician 70 (2) 129-133
* </li>
* <li>
* Wikipedia (2018): Probability Integral Transform
* https://en.wikipedia.org/wiki/Probability_integral_transform
* </li>
* <li>
* Wikipedia (2019): p-value https://en.wikipedia.org/wiki/P-value
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ModelValidationAnalyticsLibrary.md">Model Validation Analytics Library</a></li>
* <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>
* <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>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class ProbabilityIntegralTransform
{
private java.util.Map<java.lang.Double, java.lang.Double> _pValueTestStatisticMap = null;
private java.util.Map<java.lang.Double, java.lang.Double> _testStatisticPValueMap = null;
/**
* ProbabilityIntegralTransform Constructor
*
* @param testStatisticPValueMap Test Statistic - p Value Map
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public ProbabilityIntegralTransform (
final java.util.Map<java.lang.Double, java.lang.Double> testStatisticPValueMap)
throws java.lang.Exception
{
if (null == (_testStatisticPValueMap = testStatisticPValueMap) ||
0 == _testStatisticPValueMap.size())
{
throw new java.lang.Exception ("ProbabilityIntegralTransform Constructor => Invalid Inputs");
}
_pValueTestStatisticMap = new java.util.TreeMap<java.lang.Double, java.lang.Double>();
for (java.util.Map.Entry<java.lang.Double, java.lang.Double> testStatisticPValueMapEntry :
_testStatisticPValueMap.entrySet())
{
_pValueTestStatisticMap.put (
testStatisticPValueMapEntry.getValue(),
testStatisticPValueMapEntry.getKey()
);
}
}
/**
* Retrieve the p Value - Test Statistic Map
*
* @return The p Value - Test Statistic Map
*/
public java.util.Map<java.lang.Double, java.lang.Double> pValueTestStatisticMap()
{
return _pValueTestStatisticMap;
}
/**
* Retrieve the Test Statistic - p Value Map
*
* @return The Test Statistic - p Value Map
*/
public java.util.Map<java.lang.Double, java.lang.Double> testStatisticPValueMap()
{
return _testStatisticPValueMap;
}
/**
* Compute the p-Value corresponding to the Test Statistic Instance
*
* @param testStatistic The Test Statistic Instance
*
* @return The p-Value
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double pValue (
final double testStatistic)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (testStatistic))
{
throw new java.lang.Exception ("ProbabilityIntegralTransform::pValue => Invalid Inputs");
}
java.util.Set<java.lang.Double> testStatisticKeySet = _testStatisticPValueMap.keySet();
double testStatisticKeyCurrent = java.lang.Double.NaN;
double testStatisticKeyPrevious = java.lang.Double.NaN;
for (double testStatisticKey : testStatisticKeySet)
{
if (testStatistic == testStatisticKey)
{
return _testStatisticPValueMap.get (testStatistic);
}
if (testStatistic < testStatisticKey)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (testStatisticKeyPrevious))
{
return 0.;
}
testStatisticKeyCurrent = testStatisticKey;
break;
}
testStatisticKeyPrevious = testStatisticKey;
}
return !org.drip.numerical.common.NumberUtil.IsValid (testStatisticKeyCurrent) ||
testStatistic >= testStatisticKeyCurrent ? 1. :
((testStatistic - testStatisticKeyPrevious) * _testStatisticPValueMap.get
(testStatisticKeyCurrent) +
(testStatisticKeyCurrent - testStatistic) * _testStatisticPValueMap.get
(testStatisticKeyPrevious)) /
(testStatisticKeyCurrent - testStatisticKeyPrevious);
}
/**
* Compute the Test Statistic Instance corresponding to the p-Value
*
* @param pValue The p-Value
*
* @return The Response Instance
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double testStatistic (
final double pValue)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (pValue))
{
throw new java.lang.Exception ("ProbabilityIntegralTransform::testStatistic => Invalid Inputs");
}
java.util.Set<java.lang.Double> pValueKeySet = _pValueTestStatisticMap.keySet();
double pValueKeyCurrent = java.lang.Double.NaN;
double pValueKeyPrevious = java.lang.Double.NaN;
for (double pValueKey : pValueKeySet)
{
if (pValue == pValueKey)
{
return _pValueTestStatisticMap.get (pValue);
}
if (pValue < pValueKey)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (pValueKeyPrevious))
{
return _pValueTestStatisticMap.get (pValueKey);
}
pValueKeyCurrent = pValueKey;
break;
}
pValueKeyPrevious = pValueKey;
}
return pValue >= pValueKeyCurrent ? _pValueTestStatisticMap.get (pValueKeyCurrent) :
((pValue - pValueKeyPrevious) * _pValueTestStatisticMap.get (pValueKeyCurrent) +
(pValueKeyCurrent - pValue) * _pValueTestStatisticMap.get (pValueKeyPrevious)) /
(pValueKeyCurrent - pValueKeyPrevious);
}
}