ErlangPDFEstimate.java
package org.drip.sample.gammadistribution;
import org.drip.function.definition.R1ToR1;
import org.drip.function.definition.R2ToR1;
import org.drip.measure.gamma.ErlangDistribution;
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>ErlangPDFEstimate</i> demonstrates the Construction and Analysis of the R<sup>1</sup> Erlang
* Distribution. The References are:
*
* <br><br>
* <ul>
* <li>
* Devroye, L. (1986): <i>Non-Uniform Random Variate Generation</i> <b>Springer-Verlag</b> New York
* </li>
* <li>
* Gamma Distribution (2019): Gamma Distribution
* https://en.wikipedia.org/wiki/Chi-squared_distribution
* </li>
* <li>
* Louzada, F., P. L. Ramos, and E. Ramos (2019): A Note on Bias of Closed-Form Estimators for the
* Gamma Distribution Derived From Likelihood Equations <i>The American Statistician</i> <b>73
* (2)</b> 195-199
* </li>
* <li>
* Minka, T. (2002): Estimating a Gamma distribution https://tminka.github.io/papers/minka-gamma.pdf
* </li>
* <li>
* Ye, Z. S., and N. Chen (2017): Closed-Form Estimators for the Gamma Distribution Derived from
* Likelihood Equations <i>The American Statistician</i> <b>71 (2)</b> 177-181
* </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/measure/README.md">R<sup>d</sup> Continuous/Discrete Probability Measures</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/gamma/README.md">R<sup>1</sup> Gamma Distribution Implementation/Properties</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class ErlangPDFEstimate
{
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;
double[] thetaArray =
{
1.0,
2.0,
3.0,
4.0,
5.0,
};
double[] tArray =
{
0.1,
1.0,
2.0,
3.0,
4.0,
5.0,
6.0,
7.0,
8.0,
9.0,
10.0,
12.0,
};
int[] kArray =
{
// 1,
2,
3,
4,
5,
6,
7,
8,
};
double[] pValueArray =
{
0.05,
0.10,
0.15,
0.20,
0.25,
0.30,
0.35,
0.40,
0.45,
0.50,
0.55,
0.60,
0.65,
0.70,
0.75,
0.80,
0.85,
0.90,
0.95,
0.99,
};
R1ToR1 gammaEstimator = new EulerIntegralSecondKind (
null
);
R2ToR1 lowerIncompleteGammaEstimator = LowerIncompleteGamma();
R1ToR1 digammaEstimator = CumulativeSeriesEstimator.AbramowitzStegun2007 (
digammaTermCount
);
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| PROBABILITY DENSITY FUNCTION ESTIMATE ||");
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - Shape, Scale ||");
System.out.println ("\t| - Values for different t ||");
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------||");
for (double theta : thetaArray)
{
for (int k : kArray)
{
ErlangDistribution erlangDistribution = new ErlangDistribution (
k,
theta,
gammaEstimator,
digammaEstimator,
lowerIncompleteGammaEstimator
);
String display = "\t| [" +
FormatUtil.FormatDouble (k, 1, 0, 1., false) + ", " +
FormatUtil.FormatDouble (theta, 1, 0, 1., false) +
"] =>";
for (double t : tArray)
{
display = display + " " + FormatUtil.FormatDouble (
erlangDistribution.density (
t
), 1, 5, 1., false
) + " |";
}
System.out.println (display + "|");
}
}
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------||");
System.out.println();
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| CUMULATIVE DISTRIBUTION FUNCTION ESTIMATE ||");
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - Shape, Scale ||");
System.out.println ("\t| - Values for different t ||");
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------||");
for (double theta : thetaArray)
{
for (int k : kArray)
{
ErlangDistribution erlangDistribution = new ErlangDistribution (
k,
theta,
gammaEstimator,
digammaEstimator,
lowerIncompleteGammaEstimator
);
String display = "\t| [" +
FormatUtil.FormatDouble (k, 1, 0, 1., false) + ", " +
FormatUtil.FormatDouble (theta, 1, 0, 1., false) +
"] =>";
for (double t : tArray)
{
display = display + " " + FormatUtil.FormatDouble (
erlangDistribution.cumulative (t), 1, 5, 1., false
) + " |";
}
System.out.println (display + "|");
}
}
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------||");
System.out.println();
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| INVERSE CUMULATIVE DISTRIBUTION FUNCTION ESTIMATE ||");
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - Shape, Scale ||");
System.out.println ("\t| - Values for different p ||");
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------||");
for (double theta : thetaArray)
{
for (int k : kArray)
{
ErlangDistribution erlangDistribution = new ErlangDistribution (
k,
theta,
gammaEstimator,
digammaEstimator,
lowerIncompleteGammaEstimator
);
String display = "\t| [" +
FormatUtil.FormatDouble (k, 1, 0, 1., false) + ", " +
FormatUtil.FormatDouble (theta, 1, 0, 1., false) +
"] =>";
for (double p : pValueArray)
{
display = display + " " + FormatUtil.FormatDouble (
erlangDistribution.invCumulative (p), 1, 2, 1., false
) + " |";
}
System.out.println (display + "|");
}
}
System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------||");
EnvManager.TerminateEnv();
}
}