Features:

Bug Fixes/Re-organization: - Pareto R^1 PDF and CDF (45) - Pareto R^1 Distribution - Mean Exception (58) - Pareto R^1 Distribution - Variance Exception (59, 60) Samples: - R^1 CDF and PDF #1 (1, 2, 3) - R^1 CDF and PDF #2 (4, 5, 6) - R^1 CDF and PDF #3 (7, 8, 9) - R^1 CDF and PDF #4 (10, 11, 12) - R^1 Pareto Quantile Variates #1 (13, 14, 15) - R^1 Pareto Quantile Variates #2 (16, 17, 18) - R^1 Pareto Quantile Variates #3 (19, 20, 21) - R^1 Pareto Quantile Variates #4 (22, 23, 24) - R^1 Pareto Quantile Variates #5 (25, 26, 27) - R^1 Pareto Quantile Variates #6 (28, 29, 30) - R^1 Pareto Quantile Variates #7 (31, 32, 33) - R^1 Pareto Quantile Variates #8 (33, 34, 36) - R^1 Pareto Quantile Variates #9 (37, 38, 39) - R^1 Pareto Quantile Variates #10 (40, 41, 42) - R^1 Pareto Quantile Variates #11 (43, 44) - R^1 Pareto Distribution Statistics #1 (46, 47, 48) - R^1 Pareto Distribution Statistics #2 (49, 50, 51) - R^1 Pareto Distribution Statistics #3 (52, 53, 54) - R^1 Pareto Distribution Statistics #4 (55, 56, 57) IdeaDRIP:
lakshmiDRIP · Aug 17, 2023 · d81a46a · d81a46a
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diff --git a/ReleaseNotes/12_29_2022.txt b/ReleaseNotes/12_29_2022.txt
@@ -0,0 +1,34 @@
+
+Features:
+
+Bug Fixes/Re-organization:
+
+ - Pareto R^1 PDF and CDF (45)
+ - Pareto R^1 Distribution - Mean Exception (58)
+ - Pareto R^1 Distribution - Variance Exception (59, 60)
+
+
+Samples:
+
+ - R^1 CDF and PDF #1 (1, 2, 3)
+ - R^1 CDF and PDF #2 (4, 5, 6)
+ - R^1 CDF and PDF #3 (7, 8, 9)
+ - R^1 CDF and PDF #4 (10, 11, 12)
+ - R^1 Pareto Quantile Variates #1 (13, 14, 15)
+ - R^1 Pareto Quantile Variates #2 (16, 17, 18)
+ - R^1 Pareto Quantile Variates #3 (19, 20, 21)
+ - R^1 Pareto Quantile Variates #4 (22, 23, 24)
+ - R^1 Pareto Quantile Variates #5 (25, 26, 27)
+ - R^1 Pareto Quantile Variates #6 (28, 29, 30)
+ - R^1 Pareto Quantile Variates #7 (31, 32, 33)
+ - R^1 Pareto Quantile Variates #8 (33, 34, 36)
+ - R^1 Pareto Quantile Variates #9 (37, 38, 39)
+ - R^1 Pareto Quantile Variates #10 (40, 41, 42)
+ - R^1 Pareto Quantile Variates #11 (43, 44)
+ - R^1 Pareto Distribution Statistics #1 (46, 47, 48)
+ - R^1 Pareto Distribution Statistics #2 (49, 50, 51)
+ - R^1 Pareto Distribution Statistics #3 (52, 53, 54)
+ - R^1 Pareto Distribution Statistics #4 (55, 56, 57)
+
+
+IdeaDRIP:
diff --git a/ScheduleSheet.xlsx b/ScheduleSheet.xlsx
diff --git a/src/main/java/org/drip/measure/continuous/R1ParetoDistribution.java b/src/main/java/org/drip/measure/continuous/R1ParetoDistribution.java
@@ -218,17 +218,61 @@ public double lambda()
  );
  }
 
+ @Override public double quantile (
+ final double p)
+ throws Exception
+ {
+ if (!NumberUtil.IsValid (
+ p
+ ) || 0. > p || 1. < p
+ )
+ {
+ throw new Exception (
+ "R1ParetoDistribution::quantile => p is Invalid"
+ );
+ }
+
+ if (0. == p)
+ {
+ return support()[0];
+ }
+
+ if (1. == p)
+ {
+ return support()[1];
+ }
+
+ return _k + Math.pow (
+ 1. - p,
+ -1. * _lambda
+ );
+ }
+
  @Override public double mean()
  throws Exception
  {
- return _lambda * _k / (1. >= _lambda ? 1. - _lambda : _lambda - 1.);
+ if (1. >= _lambda)
+ {
+ throw new Exception (
+ "R1ParetoDistribution::mean => Does not converge for lambda <= 1."
+ );
+ }
+
+ return _lambda * _k / _lambda - 1.;
  }
 
  @Override public double variance()
  throws Exception
  {
+ if (1. >= _lambda)
+ {
+ throw new Exception (
+ "R1ParetoDistribution::variance => Does not converge for lambda <= 2."
+ );
+ }
+
  double mean = mean();
 
- return _lambda * _k * _k / (2. >= _lambda ? 2. - _lambda : _lambda - 2.) - mean * mean;
+ return _lambda * _k * _k / (_lambda - 2.) - mean * mean;
  }
 }
diff --git a/src/main/java/org/drip/sample/pareto/R1PDFAndCDF.java b/src/main/java/org/drip/sample/pareto/R1PDFAndCDF.java
@@ -0,0 +1,254 @@
+
+package org.drip.sample.pareto;
+
+import org.drip.measure.continuous.R1ParetoDistribution;
+import org.drip.service.common.FormatUtil;
+import org.drip.service.env.EnvManager;
+
+/*
+ * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+ */
+
+/*!
+ * Copyright (C) 2023 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,
+ * graph builder/navigator, 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
+ * - Graph Algorithm
+ * - 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
+ * 
+ * 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>R1PDFAndCDF</i> illustrates the Density and CDF Metrics Suite generated from R<sup>1</sup> Pareto
+ * 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>
+ * Exponential Distribution (2019): Exponential Distribution
+ * https://en.wikipedia.org/wiki/Exponential_distribution
+ * </li>
+ * <li>
+ * Norton, M., V. Khokhlov, and S. Uryasev (2019): Calculating CVaR and bPOE for Common Probability
+ * Distributions with Application to Portfolio Optimization and Density Estimation <i>Annals of
+ * Operations Research</i> <b>299 (1-2)</b> 1281-1315
+ * </li>
+ * <li>
+ * Ross, S. M. (2009): <i>Introduction to Probability and Statistics for Engineers and Scientists
+ * 4<sup>th</sup> Edition</i> <b>Associated Press</b> New York, NY
+ * </li>
+ * <li>
+ * Schmidt, D. F., and D. Makalic (2009): Universal Models for the Exponential Distribution <i>IEEE
+ * Transactions on Information Theory</i> <b>55 (7)</b> 3087-3090
+ * </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/exponential/README.md">R<sup>1</sup> Exponential Distribution Implementation/Properties</a></li>
+ * </ul>
+ *
+ * @author Lakshmi Krishnamurthy
+ */
+
+public class R1PDFAndCDF
+{
+
+ /**
+ * Entry Point
+ * 
+ * @param argumentArray Command Line Argument Array
+ * 
+ * @throws Exception Thrown on Error/Exception Situation
+ */
+
+ public static final void main (
+ final String[] argumentArray)
+ throws Exception
+ {
+ EnvManager.InitEnv ("");
+
+ double[] horizonArray = {1./12., 0.25, 0.5, 1., 2., 3., 5., 10.};
+ double[] kArray = {0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1., 2., 3., 4., 5.};
+ double[] lambdaArray = {0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1., 2., 3., 4., 5.};
+
+ System.out.println (
+ "\t||---------------------------------------------------------------------------------------------------------------||"
+ );
+
+ System.out.println (
+ "\t|| Probability Density across Horizon ||"
+ );
+
+ System.out.println (
+ "\t||---------------------------------------------------------------------------------------------------------------||"
+ );
+
+ System.out.println (
+ "\t|| L -> R:"
+ );
+
+ System.out.println (
+ "\t|| - [Lambda, k] (Left-most Values)"
+ );
+
+ System.out.println (
+ "\t|| - Probability Density across Time Horizons (Right-most columns)"
+ );
+
+ System.out.println (
+ "\t||---------------------------------------------------------------------------------------------------------------||"
+ );
+
+ for (int i = 0; i < kArray.length; ++i)
+ {
+ for (int j = 0; j < lambdaArray.length; ++j)
+ {
+ String metricDisplay = "\t|| [" + FormatUtil.FormatDouble (
+ kArray[i], 1, 2, 1., false
+ ) + ", " +FormatUtil.FormatDouble (
+ lambdaArray[j], 1, 2, 1., false
+ ) + "] =>";
+
+ R1ParetoDistribution paretoDistribution = new R1ParetoDistribution (lambdaArray[j], kArray[i]);
+
+ for (int k = 0; k < horizonArray.length; ++k)
+ {
+ metricDisplay += " " + FormatUtil.FormatDouble (
+ paretoDistribution.density (horizonArray[k] + kArray[i]), 1, 6, 1.
+ ) + " |";
+ }
+
+ System.out.println (metricDisplay + "|");
+ }
+ }
+
+ System.out.println (
+ "\t||---------------------------------------------------------------------------------------------------------------||"
+ );
+
+ System.out.println();
+
+ System.out.println (
+ "\t||---------------------------------------------------------------------------------------------------------------||"
+ );
+
+ System.out.println (
+ "\t|| Cumulative Probability across Horizon ||"
+ );
+
+ System.out.println (
+ "\t||---------------------------------------------------------------------------------------------------------------||"
+ );
+
+ System.out.println (
+ "\t|| L -> R:"
+ );
+
+ System.out.println (
+ "\t|| - [Lambda, k] (Left-most Values)"
+ );
+
+ System.out.println (
+ "\t|| - Probability Density across Time Horizons (Right-most columns)"
+ );
+
+ System.out.println (
+ "\t||---------------------------------------------------------------------------------------------------------------||"
+ );
+
+ for (int i = 0; i < kArray.length; ++i)
+ {
+ for (int j = 0; j < lambdaArray.length; ++j)
+ {
+ String metricDisplay = "\t|| [" + FormatUtil.FormatDouble (
+ kArray[i], 1, 2, 1., false
+ ) + ", " +FormatUtil.FormatDouble (
+ lambdaArray[j], 1, 2, 1., false
+ ) + "] =>";
+
+ R1ParetoDistribution paretoDistribution = new R1ParetoDistribution (lambdaArray[j], kArray[i]);
+
+ for (int k = 0; k < horizonArray.length; ++k)
+ {
+ metricDisplay += " " + FormatUtil.FormatDouble (
+ paretoDistribution.cumulative (horizonArray[k] + kArray[i]), 1, 6, 1.
+ ) + " |";
+ }
+
+ System.out.println (metricDisplay + "|");
+ }
+ }
+
+ System.out.println (
+ "\t||---------------------------------------------------------------------------------------------------------------||"
+ );
+
+ EnvManager.TerminateEnv();
+ }
+}