StandardNormalTStatistic.java
package org.drip.sample.samplestatistics;
import org.drip.measure.gaussian.R1UnivariateNormal;
import org.drip.measure.statistics.PopulationCentralMeasures;
import org.drip.measure.statistics.UnivariateMoments;
import org.drip.numerical.common.FormatUtil;
import org.drip.numerical.common.StringUtil;
import org.drip.service.env.EnvManager;
/*
* -*- 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>StandardNormalTStatistic</i> illustrates the Computation of the t-statistic, z-score, and other
* related Metrics of the Sample/Population Mean for an Empirical Standard Normal Distribution.
*
* <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>
* Wikipedia (2018): Probability Integral Transform
* https://en.wikipedia.org/wiki/Probability_integral_transform
* </li>
* <li>
* Wikipedia (2018): t-statistic https://en.wikipedia.org/wiki/T-statistic
* </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/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/sample">Sample</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/hypothesistest">Statistical Hypothesis Tests</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class StandardNormalTStatistic
{
private static final double UnivariateRandom()
throws Exception
{
return R1UnivariateNormal.Standard().random();
}
private static final PopulationCentralMeasures PopulationMeasures()
{
return R1UnivariateNormal.Standard().populationCentralMeasures();
}
private static final double SampleMeanEstimate (
final int count)
throws Exception
{
double[] univariateRandomArray = new double[count];
for (int index = 0; index < count; ++index)
{
univariateRandomArray[index] = UnivariateRandom();
}
return UnivariateMoments.Standard (
StringUtil.GUID(),
univariateRandomArray,
null
).mean();
}
private static final UnivariateMoments SampleStatistics (
final int drawCount,
final int sampleCount)
throws Exception
{
double[] sampleMeanEstimateArray = new double[sampleCount];
for (int sampleIndex = 0; sampleIndex < sampleCount; ++sampleIndex)
{
sampleMeanEstimateArray[sampleIndex] = SampleMeanEstimate (drawCount);
}
return UnivariateMoments.Standard (
StringUtil.GUID(),
sampleMeanEstimateArray,
null
);
}
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
int drawCount = 10000;
int sampleCount = 200;
UnivariateMoments sampleStatistics = SampleStatistics (
drawCount,
sampleCount
);
PopulationCentralMeasures populationCentralMeasures = PopulationMeasures();
double nextDraw = UnivariateRandom();
double updatedMean = (sampleStatistics.mean() * sampleCount + nextDraw) / (sampleCount + 1);
System.out.println ("\t|--------------------------------------------------||");
System.out.println ("\t| STANDARD UNIFORM DISTRIBUTION ||");
System.out.println ("\t|--------------------------------------------------||");
System.out.println (
"\t| Population Mean => " +
FormatUtil.FormatDouble (populationCentralMeasures.mean(), 1, 8, 1.)
);
System.out.println (
"\t| Population Variance => " +
FormatUtil.FormatDouble (populationCentralMeasures.variance(), 1, 8, 1.)
);
System.out.println ("\t|--------------------------------------------------||");
System.out.println (
"\t| Mean => " +
FormatUtil.FormatDouble (sampleStatistics.mean(), 1, 8, 1.)
);
System.out.println (
"\t| Variance => " +
FormatUtil.FormatDouble (sampleStatistics.variance(), 1, 8, 1.)
);
System.out.println (
"\t| Sample Count => " +
FormatUtil.FormatDouble (sampleStatistics.numSample(), 3, 0, 1.)
);
System.out.println (
"\t| Degrees Of Freedom => " +
FormatUtil.FormatDouble (sampleStatistics.degreesOfFreedom(), 3, 0, 1.)
);
System.out.println (
"\t| Standard Deviation => " +
FormatUtil.FormatDouble (sampleStatistics.stdDev(), 1, 8, 1.)
);
System.out.println (
"\t| Standard Error => " +
FormatUtil.FormatDouble (sampleStatistics.stdError(), 1, 8, 1.)
);
System.out.println (
"\t| Predictive Confidence Interval => " +
FormatUtil.FormatDouble (sampleStatistics.predictiveConfidenceLevel(), 1, 8, 1.)
);
System.out.println ("\t|--------------------------------------------------||");
System.out.println (
"\t| Next Draw => " +
FormatUtil.FormatDouble (nextDraw, 1, 8, 1.)
);
System.out.println (
"\t| Next Draw T-Statistics => " +
FormatUtil.FormatDouble (sampleStatistics.tStatistic (updatedMean), 1, 8, 1.)
);
System.out.println (
"\t| Standard Error Offset => " +
FormatUtil.FormatDouble (sampleStatistics.standardErrorOffset (nextDraw), 1, 0, 1.)
);
System.out.println (
"\t| Population Z-Score => " +
FormatUtil.FormatDouble (populationCentralMeasures.zScore (nextDraw), 1, 8, 1.)
);
System.out.println ("\t|--------------------------------------------------||");
EnvManager.TerminateEnv();
}
}