QQTest2.java
package org.drip.sample.quantile;
import org.drip.measure.gaussian.R1UnivariateNormal;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.validation.evidence.Ensemble;
import org.drip.validation.evidence.Sample;
import org.drip.validation.evidence.TestStatisticEvaluator;
import org.drip.validation.hypothesis.ProbabilityIntegralTransformTest;
import org.drip.validation.quantile.PlottingPositionGeneratorFilliben;
import org.drip.validation.quantile.QQTestOutcome;
import org.drip.validation.quantile.QQVertex;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2019 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
* calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
* FX, and structured products.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three main modules:
*
* - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
*
* DROP Analytics Core implements libraries for the following:
* - Fixed Income Analytics
* - Asset Backed Analytics
* - XVA Analytics
* - Exposure and Margin Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Transaction Cost Analytics
*
* DROP Numerical Core implements libraries for the following:
* - Statistical Learning Library
* - Numerical Optimizer Library
* - Machine Learning Library
* - Spline Builder Library
*
* 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
* - 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>QQTest2</i> compares the Order Statistics between 2 Similar Normal Distributions using the Filliben
* (1975) Median Based Plotting Position Generator.
*
* <br><br>
* <ul>
* <li>
* Gibbons, J. D., and S. Chakraborti (2003): <i>Non-parametric Statistical Inference 4th
* Edition</i> <b>CRC Press</b>
* </li>
* <li>
* Filliben, J. J. (1975): The Probability Plot Correlation Coefficient Test for Normality
* <i>Technometrics, American Society for Quality</i> <b>17 (1)</b> 111-117
* </li>
* <li>
* Gnanadesikan, R. (1977): <i>Methods for Statistical Analysis of Multivariate Observations</i>
* <b>Wiley</b>
* </li>
* <li>
* Thode, H. C. (2002): <i>Testing for Normality</i> <b>Marcel Dekker</b> New York
* </li>
* <li>
* Wikipedia (2018): Q-Q Plot https://en.wikipedia.org/wiki/Q%E2%80%93Q_plot
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/AnalyticsCore.md">Analytics 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">Model Validation Suite</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/validation/quantile">Quantile Based Graphical Numerical Validators</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class QQTest2
{
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 void QQPlot (
final QQTestOutcome qqTestOutcome)
throws Exception
{
QQVertex[] qqVertexArray = qqTestOutcome.qqVertexArray();
System.out.println ("\t|------------------------------------||");
System.out.println ("\t| Q-Q TEST OUTCOME ||");
System.out.println ("\t|------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - Order Statistic Ordinal ||");
System.out.println ("\t| - Order Statistic Quantile ||");
System.out.println ("\t| - Order Statistic X ||");
System.out.println ("\t| - Order Statistic Y ||");
System.out.println ("\t|------------------------------------||");
for (QQVertex qqVertex : qqVertexArray)
{
System.out.println (
"\t| " + FormatUtil.FormatDouble (
qqVertex.plottingPosition().orderStatisticOrdinal(), 2, 0, 1.
) + " => " +
FormatUtil.FormatDouble (qqVertex.plottingPosition().quantile(), 1, 4, 1.) + " | " +
FormatUtil.FormatDouble (qqVertex.orderStatisticX(), 1, 4, 1.) + " | " +
FormatUtil.FormatDouble (qqVertex.orderStatisticY(), 1, 4, 1.) + " ||"
);
}
System.out.println ("\t|------------------------------------||");
System.out.println ("\t|-----------------------------------------------------||");
System.out.println (
"\t| Probability Plot Correlation Coefficient => " +
FormatUtil.FormatDouble (qqTestOutcome.probabilityPlotCorrelationCoefficient(), 1, 4, 1.) + " ||"
);
System.out.println ("\t|-----------------------------------------------------||");
}
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
int drawCount = 1000000;
int sampleCount = 1;
double sampleMean = 0.;
double hypothesisMean = 0.;
int orderStatisticCount = 25;
double sampleVolatility = 1.0;
double hypothesisVolatility = 1.0;
PlottingPositionGeneratorFilliben plottingPositionGenerator = new
PlottingPositionGeneratorFilliben (orderStatisticCount);
Sample sample = GenerateSample (
sampleMean,
sampleVolatility,
drawCount
);
Ensemble hypothesis = GenerateEnsemble (
hypothesisMean,
hypothesisVolatility,
drawCount,
sampleCount
);
QQPlot (
new ProbabilityIntegralTransformTest (
hypothesis.nativeProbabilityIntegralTransform()
).qqTest (
sample.nativeProbabilityIntegralTransform(),
plottingPositionGenerator
)
);
EnvManager.TerminateEnv();
}
}