CumulativeBinomialDistributionProperty.java
package org.drip.sample.beta;
import org.drip.function.definition.R1PropertyVerification;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.specialfunction.property.IncompleteBetaEqualityLemma;
/*
* -*- 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>CumulativeBinomialDistributionProperty</i> illustrates the Verification of the Cumulative Binomial
* Distribution Property. 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 CumulativeBinomialDistributionProperty
{
private static final void Verifier (
final double p,
final double n,
final double k)
throws Exception
{
R1PropertyVerification verification =
IncompleteBetaEqualityLemma.CumulativeBinomialDistribution().verify (
p,
n,
k
);
System.out.println (
"\t| {p=" + FormatUtil.FormatDouble (p, 1, 2, 1., false) + "; n=" +
FormatUtil.FormatDouble (n, 2, 0, 1., false) + ", k=" +
FormatUtil.FormatDouble (k, 2, 0, 1., false) + "} => " +
FormatUtil.FormatDouble (verification.lValue(), 1, 10, 1.) + " | " +
FormatUtil.FormatDouble (verification.rValue(), 1, 10, 1.) + " | " +
verification.verified() + " ||"
);
}
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv ("");
double[] pArray =
{
1.00,
0.80,
0.60,
0.40,
0.20,
};
double[] nArray =
{
99,
};
double[] kArray =
{
5,
10,
15,
20,
25,
30,
35,
40,
45,
50,
55,
60,
65,
70,
75,
80,
85,
90,
95,
};
System.out.println ("\t|--------------------------------------------------------------||");
System.out.println ("\t| CUMULATIVE BINOMIAL DISTRIBUTION PROPERTY ||");
System.out.println ("\t|--------------------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - p ||");
System.out.println ("\t| - n ||");
System.out.println ("\t| - k ||");
System.out.println ("\t| - LHS Value ||");
System.out.println ("\t| - RHS Value ||");
System.out.println ("\t| - Verification Success? ||");
System.out.println ("\t|--------------------------------------------------------------||");
for (double p : pArray)
{
for (double n : nArray)
{
for (double k : kArray)
{
Verifier (
p,
n,
k
);
}
}
}
System.out.println ("\t|--------------------------------------------------------------||");
EnvManager.TerminateEnv();
}
}