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- Exponential To R^1 Pareto #1 (1, 2, 3) - Exponential To R^1 Pareto #2 (4, 5, 6) - R^1 Exponential To Pareto Shell (9, 10) - R^1 Exponential To Pareto Normalizer (11, 12) - R^1 Exponential To Pareto Lambda (13, 14) - R^1 Exponential To Pareto k (15, 16) - R^1 Pareto Distribution Normalizer Estimation (17, 18) - Exponential To R^1 Pareto #3 (19, 20, 21) - R^1 Exponential To Pareto Constructor (24, 25, 26) - R^1 Exponential To Pareto Support (27, 28) - R^1 Exponential To Pareto Density (29, 30) - Exponential To R^1 Pareto #4 (31, 32, 33) - R^1 Exponential To Pareto Cumulative (34, 35, 36) - R^1 Exponential To Pareto Mean #1 (37, 38, 39) - R^1 Exponential To Pareto Mean #2 (40, 41, 42) - R^1 Exponential To Pareto Variance #1 (43, 44, 45) - R^1 Exponential To Pareto Variance #2 (46, 47, 48) - R^1 Pareto Distribution Run Sweep (52, 53) Bug Fixes/Re-organization: - R^1 Gamma To Maxwell Boltzmann Squared (7) - R^1 Gamma To Exponential (8) - Trim Pareto Distribution Normalizer (22, 23) - Rename To R^1 Pareto Distribution (49, 50, 51) Samples: - R^1 CDF and PDF #1 (54, 55, 56) - R^1 CDF and PDF #2 (57, 58) - R^1 CDF and PDF #3 (59, 60) IdeaDRIP:
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| Features: | ||
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| - Exponential To R^1 Pareto #1 (1, 2, 3) | ||
| - Exponential To R^1 Pareto #2 (4, 5, 6) | ||
| - R^1 Exponential To Pareto Shell (9, 10) | ||
| - R^1 Exponential To Pareto Normalizer (11, 12) | ||
| - R^1 Exponential To Pareto Lambda (13, 14) | ||
| - R^1 Exponential To Pareto k (15, 16) | ||
| - R^1 Pareto Distribution Normalizer Estimation (17, 18) | ||
| - Exponential To R^1 Pareto #3 (19, 20, 21) | ||
| - R^1 Exponential To Pareto Constructor (24, 25, 26) | ||
| - R^1 Exponential To Pareto Support (27, 28) | ||
| - R^1 Exponential To Pareto Density (29, 30) | ||
| - Exponential To R^1 Pareto #4 (31, 32, 33) | ||
| - R^1 Exponential To Pareto Cumulative (34, 35, 36) | ||
| - R^1 Exponential To Pareto Mean #1 (37, 38, 39) | ||
| - R^1 Exponential To Pareto Mean #2 (40, 41, 42) | ||
| - R^1 Exponential To Pareto Variance #1 (43, 44, 45) | ||
| - R^1 Exponential To Pareto Variance #2 (46, 47, 48) | ||
| - R^1 Pareto Distribution Run Sweep (52, 53) | ||
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| Bug Fixes/Re-organization: | ||
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| - R^1 Gamma To Maxwell Boltzmann Squared (7) | ||
| - R^1 Gamma To Exponential (8) | ||
| - Trim Pareto Distribution Normalizer (22, 23) | ||
| - Rename To R^1 Pareto Distribution (49, 50, 51) | ||
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| Samples: | ||
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| - R^1 CDF and PDF #1 (54, 55, 56) | ||
| - R^1 CDF and PDF #2 (57, 58) | ||
| - R^1 CDF and PDF #3 (59, 60) | ||
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| IdeaDRIP: |
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src/main/java/org/drip/measure/continuous/R1ParetoDistribution.java
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| package org.drip.measure.continuous; | ||
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| import org.drip.numerical.common.NumberUtil; | ||
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| /* | ||
| * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- | ||
| */ | ||
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| /*! | ||
| * 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. | ||
| */ | ||
|
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| /** | ||
| * <i>R1ParetoDistribution</i> implements the 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 | ||
| */ | ||
|
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| public class R1ParetoDistribution | ||
| extends R1Univariate | ||
| { | ||
| private double _k = Double.NaN; | ||
| private double _lambda = Double.NaN; | ||
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| /** | ||
| * R1ParetoDistribution Constructor | ||
| * | ||
| * @param lambda Rate Parameter | ||
| * @param k K Parameter | ||
| * | ||
| * @throws Exception Thrown if the Inputs are invalid | ||
| */ | ||
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| public R1ParetoDistribution ( | ||
| final double lambda, | ||
| final double k) | ||
| throws Exception | ||
| { | ||
| if (!NumberUtil.IsValid ( | ||
| _lambda = lambda | ||
| ) || 0. >= _lambda || !NumberUtil.IsValid ( | ||
| _k = k | ||
| ) || 0. >= _k | ||
| ) | ||
| { | ||
| throw new Exception ( | ||
| "R1ParetoDistribution Constructor => Invalid Inputs" | ||
| ); | ||
| } | ||
| } | ||
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| /** | ||
| * Retrieve k | ||
| * | ||
| * @return k | ||
| */ | ||
| public double k() | ||
| { | ||
| return _k; | ||
| } | ||
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| /** | ||
| * Retrieve Lambda | ||
| * | ||
| * @return Lambda | ||
| */ | ||
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| public double lambda() | ||
| { | ||
| return _lambda; | ||
| } | ||
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| @Override public double[] support() | ||
| { | ||
| return new double[] | ||
| { | ||
| _k, | ||
| Double.POSITIVE_INFINITY | ||
| }; | ||
| } | ||
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| @Override public double density ( | ||
| final double t) | ||
| throws Exception | ||
| { | ||
| if (!supported ( | ||
| t | ||
| )) | ||
| { | ||
| throw new Exception ( | ||
| "R1ParetoDistribution::density => Variate not in Range" | ||
| ); | ||
| } | ||
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| return _lambda * Math.pow ( | ||
| _k, | ||
| _lambda | ||
| ) * Math.pow ( | ||
| t, | ||
| -1. - _lambda | ||
| ); | ||
| } | ||
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| @Override public double cumulative ( | ||
| final double t) | ||
| throws Exception | ||
| { | ||
| if (!supported ( | ||
| t | ||
| )) | ||
| { | ||
| throw new Exception ( | ||
| "R1ParetoDistribution::cumulative => Variate not in Range" | ||
| ); | ||
| } | ||
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| return 1. - Math.pow ( | ||
| _k / t, | ||
| _lambda | ||
| ); | ||
| } | ||
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| @Override public double mean() | ||
| throws Exception | ||
| { | ||
| return _lambda * _k / (1. >= _lambda ? 1. - _lambda : _lambda - 1.); | ||
| } | ||
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| @Override public double variance() | ||
| throws Exception | ||
| { | ||
| double mean = mean(); | ||
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| return _lambda * _k * _k / (2. >= _lambda ? 2. - _lambda : _lambda - 2.) - mean * mean; | ||
| } | ||
| } |
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