CentralMomentsAboutZero.java
package org.drip.sample.chisquaredistribution;
import org.drip.function.definition.R1ToR1;
import org.drip.function.definition.R2ToR1;
import org.drip.measure.chisquare.R1Central;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
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>CentralMomentsAboutZero</i> illustrates the Computation of the non-Central Moments about Zero for the
* Central Chi-squared Function. The References are:
*
* <br><br>
* <ul>
* <li>
* Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
* on Mathematics</b>
* </li>
* <li>
* Backstrom, T., and J. Fischer (2018): Fast Randomization for Distributed Low Bit-rate Coding of
* Speech and Audio <i>IEEE/ACM Transactions on Audio, Speech, and Language Processing</i> <b>26
* (1)</b> 19-30
* </li>
* <li>
* Chi-Squared Distribution (2019): Chi-Squared Function
* https://en.wikipedia.org/wiki/Chi-squared_distribution
* </li>
* <li>
* Johnson, N. L., S. Kotz, and N. Balakrishnan (1994): <i>Continuous Univariate Distributions
* 2<sup>nd</sup> Edition</i> <b>John Wiley and Sons</b>
* </li>
* <li>
* National Institute of Standards and Technology (2019): Chi-Squared Distribution
* https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm
* </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 CentralMomentsAboutZero
{
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[] mArray =
{
0,
1,
2,
3,
4,
5,
6,
7,
8,
};
int[] dofArray =
{
// 1,
2,
3,
4,
5,
6,
7,
8,
9,
};
R1ToR1 gammaEstimator = new EulerIntegralSecondKind (null);
R2ToR1 lowerIncompleteGammaEstimator = LowerIncompleteGamma();
R1ToR1 digammaEstimator = CumulativeSeriesEstimator.AbramowitzStegun2007 (digammaTermCount);
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| NON-CENTRAL MOMENT ESTIMATE ||");
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - Degrees of Freedom ||");
System.out.println ("\t| - Values for different t ||");
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------||");
for (int dof : dofArray)
{
R1Central r1Univariate = new R1Central (
dof,
gammaEstimator,
digammaEstimator,
lowerIncompleteGammaEstimator
);
String display = "\t| [" + FormatUtil.FormatDouble (dof, 1, 0, 1., false) + "] =>";
for (int m : mArray)
{
display = display + " " + FormatUtil.FormatDouble (
r1Univariate.nonCentralMoment (m), 10, 0, 1., false
) + " |";
}
System.out.println (display + "|");
}
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------||");
System.out.println();
EnvManager.TerminateEnv();
}
}