NormalAndersonDarlingGapAnalysis.java
package org.drip.sample.distancetest;
import org.drip.measure.gaussian.R1UnivariateNormal;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.validation.distance.GapTestOutcome;
import org.drip.validation.distance.GapTestSetting;
import org.drip.validation.distance.GapLossWeightFunction;
import org.drip.validation.evidence.Ensemble;
import org.drip.validation.evidence.Sample;
import org.drip.validation.evidence.TestStatisticEvaluator;
import org.drip.validation.hypothesis.HistogramTestOutcome;
import org.drip.validation.hypothesis.HistogramTestSetting;
import org.drip.validation.hypothesis.ProbabilityIntegralTransformTest;
import org.drip.validation.quantile.PlottingPositionGenerator;
import org.drip.validation.quantile.PlottingPositionGeneratorHeuristic;
/*
* -*- 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>NormalAndersonDarlingGapAnalysis</i> demonstrates the Generation of the Sample Distance Metrics for
* Different Ensemble Hypotheses.
*
* <br><br>
* <ul>
* <li>
* <b>Reference Distribution </b> - <i>Univariate Normal</i>
* </li>
* <li>
* <b>Gap Loss Function </b> - <i>Anfuso, Karyampas, and Nawroth (2017)</i>
* </li>
* <li>
* <b>Gap Loss Weight Function</b> - <i>Anderson and Darling</i>
* </li>
* </ul>
*
* <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): Discounting, LIBOR, CVA, and Funding: Interest Rate and Credit
* Pricing, Palgrave Macmillan
* </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/sample/README.md">DROP API Construction and Usage</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/validation">Empirical Univariate Gap Distance Tests</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class NormalAndersonDarlingGapAnalysis
{
private static final double UnivariateRandom (
final double mean,
final double sigma)
throws Exception
{
return new R1UnivariateNormal (
mean,
sigma
).random();
}
private static final Sample GenerateSample (
final double mean,
final double sigma,
final int drawCount)
throws Exception
{
double[] univariateRandomArray = new double[drawCount];
for (int drawIndex = 0; drawIndex < drawCount; ++drawIndex)
{
univariateRandomArray[drawIndex] = UnivariateRandom (
mean,
sigma
);
}
return new Sample (univariateRandomArray);
}
private static final Sample[] GenerateSampleArray (
final double mean,
final double sigma,
final int drawCount,
final int sampleCount)
throws Exception
{
Sample[] sampleArray = new Sample[sampleCount];
for (int sampleIndex = 0; sampleIndex < sampleCount; ++sampleIndex)
{
sampleArray[sampleIndex] = GenerateSample (
mean,
sigma,
drawCount
);
}
return sampleArray;
}
private static final Ensemble GenerateEnsemble (
final double mean,
final double sigma,
final int drawCount,
final int sampleCount)
throws Exception
{
return new Ensemble (
GenerateSampleArray (
mean,
sigma,
drawCount,
sampleCount
),
new TestStatisticEvaluator[]
{
new TestStatisticEvaluator()
{
public double evaluate (
final double[] drawArray)
throws Exception
{
return 1.;
}
}
}
);
}
private static final GapTestOutcome DistanceTest (
final Sample sample,
final Ensemble ensemble,
final GapTestSetting gapTestSetting)
throws Exception
{
return new ProbabilityIntegralTransformTest (
ensemble.nativeProbabilityIntegralTransform()
).distanceTest (
sample.nativeProbabilityIntegralTransform(),
gapTestSetting
);
}
private static final void DistanceTest (
final double hypothesisMean,
final double hypothesisSigma,
final int drawCount,
final int sampleCount,
final Sample sample,
final GapTestSetting gapTestSetting,
final PlottingPositionGenerator plottingPositionGenerator)
throws Exception
{
Ensemble hypothesis = GenerateEnsemble (
hypothesisMean,
hypothesisSigma,
drawCount,
sampleCount
);
GapTestOutcome gapTestOutcome = DistanceTest (
sample,
hypothesis,
gapTestSetting
);
HistogramTestOutcome histogram = new ProbabilityIntegralTransformTest (
gapTestOutcome.probabilityIntegralTransformWeighted()
).histogramTest (
HistogramTestSetting.AnfusoKaryampasNawroth2017 (
plottingPositionGenerator
)
);
double[] pValueIncrementalArray = histogram.pValueIncrementalArray();
double[] pValueCumulativeArray = histogram.pValueCumulativeArray();
double thresholdTestStatistic = histogram.thresholdTestStatistic();
double[] gapArray = histogram.testStatisticArray();
double distance = gapTestOutcome.distance();
System.out.println ("\t|--------------------------------------------------------------------||");
System.out.println ("\t| Normal Anfuso Karyampas Nawroth Distance Test ||");
System.out.println ("\t|--------------------------------------------------------------------||");
System.out.println (
"\t| Mean => [" + FormatUtil.FormatDouble (hypothesisMean, 1, 8, 1.) +
"] | Sigma => [" + FormatUtil.FormatDouble (hypothesisSigma, 1, 8, 1.) + "] ||"
);
System.out.println ("\t|--------------------------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - Weighted Distance Metric ||");
System.out.println ("\t| - Cumulative p-Value ||");
System.out.println ("\t| - Incremental p-Value ||");
System.out.println ("\t| - Ensemble Weighted Distance ||");
System.out.println ("\t| - p-Value Threshold Distance ||");
System.out.println ("\t|--------------------------------------------------------------------||");
for (int histogramIndex = 0;
histogramIndex <= plottingPositionGenerator.orderStatisticCount() + 1;
++histogramIndex)
{
System.out.println (
"\t|" +
FormatUtil.FormatDouble (gapArray[histogramIndex], 1, 8, 1.) + " | " +
FormatUtil.FormatDouble (pValueCumulativeArray[histogramIndex], 1, 8, 1.) + " | " +
FormatUtil.FormatDouble (pValueIncrementalArray[histogramIndex], 1, 8, 1.) + " | " +
FormatUtil.FormatDouble (distance, 1, 8, 1.) + " | " +
FormatUtil.FormatDouble (thresholdTestStatistic, 1, 8, 1.) + " ||"
);
}
System.out.println ("\t|--------------------------------------------------------------------||");
}
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
int drawCount = 2000;
int sampleCount = 600;
double sampleMean = 0.;
double sampleSigma = 1.;
int orderStatisticsCount = 20;
double[] hypothesisMeanArray = {
-0.50,
-0.25,
0.00,
0.25,
0.50
};
double[] hypothesisSigmaArray = {
0.50,
0.75,
1.00,
1.25,
1.50
};
GapTestSetting gapTestSetting = GapTestSetting.RiskFactorLossTest
(GapLossWeightFunction.AndersonDarling());
PlottingPositionGenerator plottingPositionGenerator = PlottingPositionGeneratorHeuristic.NIST2013
(orderStatisticsCount);
Sample sample = GenerateSample (
sampleMean,
sampleSigma,
drawCount
);
for (double hypothesisMean : hypothesisMeanArray)
{
for (double hypothesisSigma : hypothesisSigmaArray)
{
DistanceTest (
hypothesisMean,
hypothesisSigma,
drawCount,
sampleCount,
sample,
gapTestSetting,
plottingPositionGenerator
);
}
}
EnvManager.TerminateEnv();
}
}