AsymptoticEstimate.java
package org.drip.sample.beta;
import org.drip.function.definition.R2ToR1;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.specialfunction.beta.AsymptoticLogEstimator;
import org.drip.specialfunction.beta.LogGammaEstimator;
import org.drip.specialfunction.loggamma.NemesAnalyticEstimator;
/*
* -*- 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>AsymptoticEstimate</i> illustrates the Estimation and the Comparison of Asymptotic Estimates of the
* Beta 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>
* Davis, P. J. (1959): Leonhard Euler's Integral: A Historical Profile of the Gamma Function
* <i>American Mathematical Monthly</i> <b>66 (10)</b> 849-869
* </li>
* <li>
* Whitaker, E. T., and G. N. Watson (1996): <i>A Course on Modern Analysis</i> <b>Cambridge
* University Press</b> New York
* </li>
* <li>
* Wikipedia (2019): Beta Function https://en.wikipedia.org/wiki/Beta_function
* </li>
* <li>
* Wikipedia (2019): Gamma Function https://en.wikipedia.org/wiki/Gamma_function
* </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/FunctionAnalysisLibrary.md">Function 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/beta/README.md">Estimates of the Beta Functions</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class AsymptoticEstimate
{
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
double[] xArray =
{
5.,
10.,
15.,
20.,
25.
};
double[] yArray =
{
5.,
10.,
15.,
20.,
25.
};
int logGammaTermCount = 1000000;
R2ToR1 stirlingLogBetaEstimator = AsymptoticLogEstimator.Stirling();
LogGammaEstimator logBetaEstimator = LogGammaEstimator.Weierstrass (logGammaTermCount);
R2ToR1 largeXLogBetaEstimator = AsymptoticLogEstimator.LargeX (new NemesAnalyticEstimator (null));
System.out.println ("\t|-------------------------------------------------------------||");
System.out.println ("\t| ASYMPTOTIC ESTIMATION OF THE LOG BETA FUNCTION ||");
System.out.println ("\t|-------------------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - x ||");
System.out.println ("\t| - y ||");
System.out.println ("\t| - Log Gamma Based Log Beta Estimation ||");
System.out.println ("\t| - Stirling Asymptote Log Beta Estimation ||");
System.out.println ("\t| - Large X Asymptote Log Beta Estimation ||");
System.out.println ("\t|-------------------------------------------------------------||");
for (double x : xArray)
{
for (double y : yArray)
{
System.out.println (
"\t|[" + FormatUtil.FormatDouble (x, 2, 0, 1., false) + ", " +
FormatUtil.FormatDouble (y, 2, 0, 1., false) + "] => " +
FormatUtil.FormatDouble (logBetaEstimator.evaluate (x, y), 2, 10, 1.) + " | " +
FormatUtil.FormatDouble (stirlingLogBetaEstimator.evaluate (x, y), 2, 10, 1.) + " | " +
FormatUtil.FormatDouble (largeXLogBetaEstimator.evaluate (x, y), 2, 10, 1.) + " ||"
);
}
}
System.out.println ("\t|-------------------------------------------------------------||");
EnvManager.TerminateEnv();
}
}