ImportanceWeight.java
package org.drip.validation.distance;
/*
* -*- 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>ImportanceWeight</i> weighs the Importance of each Empirical Hypothesis Outcome.
*
* <br><br>
* <ul>
* <li>
* Anfuso, F., D. Karyampas, and A. Nawroth (2017): A Sound Basel III Compliant Framework for
* Back-testing Credit Exposure Models
* https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2264620 <b>eSSRN</b>
* </li>
* <li>
* Diebold, F. X., T. A. Gunther, and A. S. Tay (1998): Evaluating Density Forecasts with
* Applications to Financial Risk Management, International Economic Review 39 (4) 863-883
* </li>
* <li>
* Kenyon, C., and R. Stamm (2012): <i>Discounting, LIBOR, CVA, and Funding: Interest Rate and
* Credit Pricing</i> <b>Palgrave Macmillan</b>
* </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/distance/README.md">Hypothesis Target Distance Test Builders</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class ImportanceWeight
{
private double _positiveExpectation = java.lang.Double.NaN;
private org.drip.measure.continuous.R1Univariate _r1Univariate = null;
/**
* Construct the Importance Weight Version based on Normal Distribution
*
* @param r1UnivariateNormal R<sup>1</sup> Normal Distribution
*
* @return The Importance Weight
*/
public static final ImportanceWeight Normal (
final org.drip.measure.gaussian.R1UnivariateNormal r1UnivariateNormal)
{
if (null == r1UnivariateNormal)
{
return null;
}
final double mean = r1UnivariateNormal.mean();
final double sigma = r1UnivariateNormal.sigma();
org.drip.measure.gaussian.R1UnivariateNormal r1UnivariateNormalStandard =
org.drip.measure.gaussian.R1UnivariateNormal.Standard();
double meanOverSigma = mean / sigma;
try
{
final double positiveExpectation = java.lang.Math.max (
mean * r1UnivariateNormalStandard.cumulative (meanOverSigma) +
sigma * r1UnivariateNormalStandard.density (meanOverSigma),
0.
);
return new ImportanceWeight (
r1UnivariateNormal,
positiveExpectation
)
{
@Override public double quantileLoading (
final double q)
throws java.lang.Exception
{
return 0. == positiveExpectation ? 0. : java.lang.Math.max (
org.drip.function.e2erf.ErrorFunctionInverse.Winitzki2008b().evaluate
(2. * q - 1.) * sigma * java.lang.Math.sqrt (2.) + mean,
0
) / positiveExpectation;
}
};
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* ImportanceWeight Constructor
*
* @param r1Univariate The Underlying R<sup>1</sup> Distribution
* @param positiveExpectation The Positive Expectation
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public ImportanceWeight (
final org.drip.measure.continuous.R1Univariate r1Univariate,
final double positiveExpectation)
throws java.lang.Exception
{
if (null == (_r1Univariate = r1Univariate) ||
!org.drip.numerical.common.NumberUtil.IsValid (_positiveExpectation = positiveExpectation) ||
0. > _positiveExpectation)
{
throw new java.lang.Exception ("ImportanceWeight Constructor => Invalid Inputs");
}
}
/**
* Retrieve the Positive Expectation
*
* @return The Positive Expectation
*/
public double positiveExpectation()
{
return _positiveExpectation;
}
/**
* Retrieve the Underlying R<sup>1</sup> Distribution
*
* @return The Underlying R<sup>1</sup> Distribution
*/
public org.drip.measure.continuous.R1Univariate r1Univariate()
{
return _r1Univariate;
}
/**
* Retrieve the Importance Weight Loading given the Quantile
*
* @param q The Quantile
*
* @return The Importance Weight Loading
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double quantileLoading (
final double q)
throws java.lang.Exception
{
return 0. == _positiveExpectation ? 0. : java.lang.Math.max (
_r1Univariate.invCumulative (q),
0
) / _positiveExpectation;
}
}