NonCentralCumulantMoments.java
package org.drip.sample.chisquaredistribution;
import org.drip.function.definition.R1ToR1;
import org.drip.function.definition.R2ToR1;
import org.drip.measure.chisquare.R1NonCentral;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.specialfunction.bessel.ModifiedFirstFrobeniusSeriesEstimator;
import org.drip.specialfunction.definition.ModifiedBesselFirstKindEstimator;
import org.drip.specialfunction.digamma.CumulativeSeriesEstimator;
import org.drip.specialfunction.gamma.EulerIntegralSecondKind;
import org.drip.specialfunction.incompletegamma.LowerEulerIntegral;
/*
* -*- 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>NonCentralCumulantMoments</i> illustrates the Computation of the Leading Cumulants and the Non-Central
* Moments. The References are:
*
* <br><br>
* <ul>
* <li>
* Johnson, N. L., S. Kotz, and N. Balakrishnan (1995): <i>Continuous Univariate Distributions
* 2<sup>nd</sup> Edition</i> <b>John Wiley and Sons</b>
* </li>
* <li>
* Muirhead, R. (2005): <i>Aspects of Multivariate Statistical Theory 2<sup>nd</sup> Edition</i>
* <b>Wiley</b>
* </li>
* <li>
* Non-central Chi-Squared Distribution (2019): Chi-Squared Function
* https://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution
* </li>
* <li>
* Sankaran, M. (1963): Approximations to the Non-Central Chi-Square Distribution <i>Biometrika</i>
* <b>50 (1-2)</b> 199-204
* </li>
* <li>
* Young, D. S. (2010): tolerance: An R Package for Estimating Tolerance Intervals <i>Journal of
* Statistical Software</i> <b>36 (5)</b> 1-39
* </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/NumericalAnalysisLibrary.md">Numerical Analysis 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/chisquaredistribution/README.md">Chi-Square Distribution Usage/Properties</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class NonCentralCumulantMoments
{
private static final R2ToR1 LowerIncompleteGamma()
throws Exception
{
return new R2ToR1()
{
@Override public double evaluate (
final double s,
final double t)
throws Exception
{
return new LowerEulerIntegral (
null,
t
).evaluate (
s
);
}
};
}
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv (
""
);
int digammaTermCount = 1000;
int besselFirstTermCount = 20;
double[] nonCentralityParameterArray =
{
0.5,
1.0,
1.5,
2.0,
2.5,
3.0,
3.5,
4.0,
};
int[] dofArray =
{
2,
3,
4,
5,
6,
7,
8,
9,
};
int[] nArray =
{
1,
2,
3,
4,
5,
6,
};
R1ToR1 gammaEstimator = new EulerIntegralSecondKind (
null
);
R2ToR1 lowerIncompleteGammaEstimator = LowerIncompleteGamma();
R1ToR1 digammaEstimator = CumulativeSeriesEstimator.AbramowitzStegun2007 (
digammaTermCount
);
ModifiedBesselFirstKindEstimator modifiedBesselFirstKindEstimator =
ModifiedFirstFrobeniusSeriesEstimator.Standard (
gammaEstimator,
besselFirstTermCount
);
System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| NON CENTRAL CHI-SQUARE CUMULANTS AND NON-CENTRAL MOMENTS ||");
System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - Degrees of Freedom; Non Centrality Parameter ||");
System.out.println ("\t| - Cumulant ||");
System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------||");
for (double nonCentralityParameter : nonCentralityParameterArray)
{
for (int dof : dofArray)
{
R1NonCentral r1UnivariateNonCentral = R1NonCentral.Standard (
dof,
nonCentralityParameter,
gammaEstimator,
digammaEstimator,
lowerIncompleteGammaEstimator,
modifiedBesselFirstKindEstimator
);
String display = "\t| [" +
FormatUtil.FormatDouble (dof, 2, 0, 1., false) + " | " +
FormatUtil.FormatDouble (nonCentralityParameter, 1, 1, 1., false) +
"] =>";
for (int n : nArray)
{
display = display + " " + FormatUtil.FormatDouble (
r1UnivariateNonCentral.cumulant (
n
), 6, 0, 1., false
) + " |";
}
System.out.println (display + "|");
}
System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------||");
}
System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------||");
System.out.println();
System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| NON CENTRAL CHI-SQUARE CUMULANTS AND NON-CENTRAL MOMENTS ||");
System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - Degrees of Freedom; Non Centrality Parameter ||");
System.out.println ("\t| - Non-central Moment ||");
System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------||");
for (double nonCentralityParameter : nonCentralityParameterArray)
{
for (int dof : dofArray)
{
R1NonCentral r1UnivariateNonCentral = R1NonCentral.Standard (
dof,
nonCentralityParameter,
gammaEstimator,
digammaEstimator,
lowerIncompleteGammaEstimator,
modifiedBesselFirstKindEstimator
);
String display = "\t| [" +
FormatUtil.FormatDouble (dof, 2, 0, 1., false) + " | " +
FormatUtil.FormatDouble (nonCentralityParameter, 1, 1, 1., false) +
"] =>";
for (int n : nArray)
{
display = display + " " + FormatUtil.FormatDouble (
r1UnivariateNonCentral.nonCentralMoment (
n
), 8, 0, 1., false
) + " |";
}
System.out.println (display + "|");
}
System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------||");
}
System.out.println ("\t|------------------------------------------------------------------------------------------------------------------------------||");
System.out.println();
EnvManager.TerminateEnv();
}
}