ShapeScalePDFEstimate.java
- package org.drip.sample.gammadistribution;
- import org.drip.function.definition.R1ToR1;
- import org.drip.function.definition.R2ToR1;
- import org.drip.measure.gamma.R1ShapeScaleDistribution;
- 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>ShapeScalePDFEstimate</i> demonstrates the Construction and Analysis of the R<sup>1</sup> Gamma
- * Distribution using the Shape/Scale Parameterization. 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/dynamics/README.md">R<sup>1</sup> Gamma Distribution Implementation/Properties</a></li>
- * </ul>
- *
- * @author Lakshmi Krishnamurthy
- */
- public class ShapeScalePDFEstimate
- {
- 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)
- {
- R1ShapeScaleDistribution gammaDistribution = R1ShapeScaleDistribution.Standard (
- 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 (
- gammaDistribution.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)
- {
- R1ShapeScaleDistribution gammaDistribution = R1ShapeScaleDistribution.Standard (
- 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 (
- gammaDistribution.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)
- {
- R1ShapeScaleDistribution gammaDistribution = R1ShapeScaleDistribution.Standard (
- 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 (
- gammaDistribution.invCumulative (p), 1, 2, 1., false
- ) + " |";
- }
- System.out.println (display + "|");
- }
- }
- System.out.println ("\t|---------------------------------------------------------------------------------------------------------------------------------||");
- EnvManager.TerminateEnv();
- }
- }