From d81a46ab22307c52cee8ce53cf5334fdc4632f4e Mon Sep 17 00:00:00 2001 From: Lakshmi Krishnamurthy Date: Thu, 17 Aug 2023 04:16:50 -0400 Subject: [PATCH] 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: --- ReleaseNotes/12_29_2022.txt | 34 +++ ScheduleSheet.xlsx | Bin 38813 -> 38693 bytes .../continuous/R1ParetoDistribution.java | 48 +++- .../org/drip/sample/pareto/R1PDFAndCDF.java | 254 ++++++++++++++++++ ...CDFAndPDF.java => R1QuantileVariates.java} | 60 ++--- .../org/drip/sample/pareto/R1Statistics.java | 221 +++++++++++++++ 6 files changed, 585 insertions(+), 32 deletions(-) create mode 100644 ReleaseNotes/12_29_2022.txt create mode 100644 src/main/java/org/drip/sample/pareto/R1PDFAndCDF.java rename src/main/java/org/drip/sample/pareto/{R1CDFAndPDF.java => R1QuantileVariates.java} (82%) create mode 100644 src/main/java/org/drip/sample/pareto/R1Statistics.java diff --git a/ReleaseNotes/12_29_2022.txt b/ReleaseNotes/12_29_2022.txt new file mode 100644 index 00000000000..2f7b8a033b7 --- /dev/null +++ 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 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z62mD$iKRTkrSV3+O5r8=kB3HmNV$W9Kvkv4;pC(CQ&e$hB2Zxwyr|Eq)F|gv7Tmc= zY?T%DAr*qV7=;o_<3U}dis5?3VT(pM*C-&3oAuwUYG7knYg`bB=6`Cjr4v*`ni8%r P0(G5smrw@vukZf=$G+7R diff --git a/src/main/java/org/drip/measure/continuous/R1ParetoDistribution.java b/src/main/java/org/drip/measure/continuous/R1ParetoDistribution.java index 8303b6da1be..502c20e9262 100644 --- 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 new file mode 100644 index 00000000000..9e90dd86edf --- /dev/null +++ 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. + */ + +/** + * R1PDFAndCDF illustrates the Density and CDF Metrics Suite generated from R1 Pareto + * Distribution. The References are: + * + *

+ *
    + *
  • + * Devroye, L. (1986): Non-Uniform Random Variate Generation Springer-Verlag New York + *
    • + *
  • + * Exponential Distribution (2019): Exponential Distribution + * https://en.wikipedia.org/wiki/Exponential_distribution + *
    • + *
  • + * Norton, M., V. Khokhlov, and S. Uryasev (2019): Calculating CVaR and bPOE for Common Probability + * Distributions with Application to Portfolio Optimization and Density Estimation Annals of + * Operations Research 299 (1-2) 1281-1315 + *
    • + *
  • + * Ross, S. M. (2009): Introduction to Probability and Statistics for Engineers and Scientists + * 4th Edition Associated Press New York, NY + *
    • + *
  • + * Schmidt, D. F., and D. Makalic (2009): Universal Models for the Exponential Distribution IEEE + * Transactions on Information Theory 55 (7) 3087-3090 + *
    • + *
+ * + *

+ * + * + * @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(); + } +} diff --git a/src/main/java/org/drip/sample/pareto/R1CDFAndPDF.java b/src/main/java/org/drip/sample/pareto/R1QuantileVariates.java similarity index 82% rename from src/main/java/org/drip/sample/pareto/R1CDFAndPDF.java rename to src/main/java/org/drip/sample/pareto/R1QuantileVariates.java index f5f484520ea..ef380203f5c 100644 --- a/src/main/java/org/drip/sample/pareto/R1CDFAndPDF.java +++ b/src/main/java/org/drip/sample/pareto/R1QuantileVariates.java @@ -2,7 +2,6 @@ package org.drip.sample.pareto; import org.drip.measure.continuous.R1ParetoDistribution; -import org.drip.measure.exponential.R1RateDistribution; import org.drip.service.common.FormatUtil; import org.drip.service.env.EnvManager; @@ -79,8 +78,8 @@ */ /** - * R1CDFAndPDF illustrates the Density and CDF Metrics Suite generated from R1 Pareto - * Distribution. The References are: + * R1QuantileVariates displays the Generation of Quantiles for the R1 Pareto Distribution. + * The References are: * *

*
    @@ -117,7 +116,7 @@ * @author Lakshmi Krishnamurthy */ -public class R1CDFAndPDF +public class R1QuantileVariates { /** @@ -134,64 +133,65 @@ public static final void main ( { EnvManager.InitEnv (""); - double[] horizonArray = {1./12., 0.25, 0.5, 1., 2., 3., 5., 10.}; + double[] pArray = {0.02, 0.26, 0.50, 0.74, 0.98}; 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||--------------------------------------------------------------------------------------------------------||" + "\t||-----------------------------------------------------------------------------------------||" ); System.out.println ( - "\t|| Probability Density across Horizon ||" + "\t|| Quantile Variates ||" ); System.out.println ( - "\t||--------------------------------------------------------------------------------------------------------||" + "\t||-----------------------------------------------------------------------------------------||" ); System.out.println ( - "\t|| L -> R:" + "\t|| L -> R:" ); System.out.println ( - "\t|| - Lambda (Left-most Value)" + "\t|| - Lambda, k [Input]" ); System.out.println ( - "\t|| - Probability Density across Time Horizons (Right-most columns)" + "\t|| - Quantile Variates [output]" ); System.out.println ( - "\t||--------------------------------------------------------------------------------------------------------||" + "\t||-----------------------------------------------------------------------------------------||" ); - for (int i = 0; i < lambdaArray.length; ++i) + for (int i = 0; i < kArray.length; ++i) { - String metricDisplay = "\t|| " + FormatUtil.FormatDouble ( - lambdaArray[i], 1, 2, 1. - ) + " =>"; - - R1ParetoDistribution paretoDistribution = new R1ParetoDistribution (lambdaArray[i], 1.); - - for (int j = 0; j < horizonArray.length; ++j) + for (int j = 0; j < lambdaArray.length; ++j) { - metricDisplay += " " + FormatUtil.FormatDouble ( - paretoDistribution.density (horizonArray[j]), 1, 6, 1. - ) + " |"; + R1ParetoDistribution paretoDistribution = new R1ParetoDistribution (lambdaArray[j], kArray[i]); + + String display = "\t|| [" + FormatUtil.FormatDouble ( + lambdaArray[j], 2, 2, 1. + ) + ", " + FormatUtil.FormatDouble ( + kArray[i], 2, 2, 1. + ) + "] =>"; + + for (int k = 0; k < pArray.length; ++k) + { + display += FormatUtil.FormatDouble ( + paretoDistribution.quantile (pArray[k]), 9, 1, 1. + ) + " |"; + } + + System.out.println (display + "|"); } - - System.out.println (metricDisplay + "|"); } System.out.println ( - "\t||--------------------------------------------------------------------------------------------------------||" + "\t||-----------------------------------------------------------------------------------------||" ); - System.out.println(); - - System.out.println(); - EnvManager.TerminateEnv(); } } diff --git a/src/main/java/org/drip/sample/pareto/R1Statistics.java b/src/main/java/org/drip/sample/pareto/R1Statistics.java new file mode 100644 index 00000000000..e124e4767f3 --- /dev/null +++ b/src/main/java/org/drip/sample/pareto/R1Statistics.java @@ -0,0 +1,221 @@ + +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. + */ + +/** + * R1Statistics illustrates the Generation of Significant Statistics for the R1 Pareto + * Distribution. The References are: + * + *

    + *
      + *
    • + * Devroye, L. (1986): Non-Uniform Random Variate Generation Springer-Verlag New York + *
      • + *
    • + * Exponential Distribution (2019): Exponential Distribution + * https://en.wikipedia.org/wiki/Exponential_distribution + *
      • + *
    • + * Norton, M., V. Khokhlov, and S. Uryasev (2019): Calculating CVaR and bPOE for Common Probability + * Distributions with Application to Portfolio Optimization and Density Estimation Annals of + * Operations Research 299 (1-2) 1281-1315 + *
      • + *
    • + * Ross, S. M. (2009): Introduction to Probability and Statistics for Engineers and Scientists + * 4th Edition Associated Press New York, NY + *
      • + *
    • + * Schmidt, D. F., and D. Makalic (2009): Universal Models for the Exponential Distribution IEEE + * Transactions on Information Theory 55 (7) 3087-3090 + *
      • + *
    + * + *

    + * + * + * @author Lakshmi Krishnamurthy + */ + +public class R1Statistics +{ + + /** + * 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[] kArray = {0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1., 2., 3., 4., 5.}; + double[] lambdaArray = {0.02, 0.05, 0.1, 0.2, 0.5, 1., 2., 3., 4., 5., 10., 20.}; + + System.out.println ( + "\t||----------------------------------------------------------------------------------||" + ); + + System.out.println ( + "\t|| L -> R:" + ); + + System.out.println ( + "\t|| - Lambda, k [Input]" + ); + + System.out.println ( + "\t|| - Mean" + ); + + System.out.println ( + "\t|| - Mode" + ); + + System.out.println ( + "\t|| - Variance" + ); + + System.out.println ( + "\t|| - Skewness" + ); + + System.out.println ( + "\t|| - Excess Kurtosis" + ); + + System.out.println ( + "\t|| - Fisher Information" + ); + + System.out.println ( + "\t|| - Inter-quantile Range (IQR)" + ); + + System.out.println ( + "\t||----------------------------------------------------------------------------------||" + ); + + for (int i = 0; i < kArray.length; ++i) + { + for (int j = 0; j < lambdaArray.length; ++j) + { + R1ParetoDistribution paretoDistribution = new R1ParetoDistribution (lambdaArray[j], kArray[i]); + + System.out.println ( + "\t|| [" + FormatUtil.FormatDouble ( + lambdaArray[j], 2, 2, 1. + ) + "," + FormatUtil.FormatDouble ( + kArray[i], 2, 2, 1. + ) + "] =>" + FormatUtil.FormatDouble ( + paretoDistribution.mean(), 2, 3, 1. + /* ) + " |" + FormatUtil.FormatDouble ( + paretoDistribution.median(), 3, 3, 1. + ) + " |" + FormatUtil.FormatDouble ( + paretoDistribution.mode(), 1, 1, 1. + ) + " |" + FormatUtil.FormatDouble ( + paretoDistribution.variance(), 4, 4, 1. + ) + " |" + FormatUtil.FormatDouble ( + paretoDistribution.skewness(), 1, 1, 1. + ) + " |" + FormatUtil.FormatDouble ( + paretoDistribution.excessKurtosis(), 2, 3, 1. + ) + " |" + FormatUtil.FormatDouble ( + paretoDistribution.fisherInformation(), 4, 4, 1. + ) + " |" + FormatUtil.FormatDouble ( + paretoDistribution.iqr(), 2, 3, 1. */ + ) + " ||" + ); + } + } + + System.out.println ( + "\t||----------------------------------------------------------------------------------||" + ); + + EnvManager.TerminateEnv(); + } +}