diff --git a/ReleaseNotes/12_28_2022.txt b/ReleaseNotes/12_28_2022.txt
new file mode 100644
index 00000000000..49b337a6e4f
--- /dev/null
+++ b/ReleaseNotes/12_28_2022.txt
@@ -0,0 +1,39 @@
+
+Features:
+
+ - 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:
diff --git a/src/main/java/org/drip/measure/continuous/R1ParetoDistribution.java b/src/main/java/org/drip/measure/continuous/R1ParetoDistribution.java
new file mode 100644
index 00000000000..8303b6da1be
--- /dev/null
+++ b/src/main/java/org/drip/measure/continuous/R1ParetoDistribution.java
@@ -0,0 +1,234 @@
+
+package org.drip.measure.continuous;
+
+import org.drip.numerical.common.NumberUtil;
+
+/*
+ * -*- 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.
+ */
+
+/**
+ * R1ParetoDistribution implements 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 R1ParetoDistribution
+ extends R1Univariate
+{
+ private double _k = Double.NaN;
+ private double _lambda = Double.NaN;
+
+ /**
+ * R1ParetoDistribution Constructor
+ *
+ * @param lambda Rate Parameter
+ * @param k K Parameter
+ *
+ * @throws Exception Thrown if the Inputs are invalid
+ */
+
+ 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"
+ );
+ }
+ }
+
+ /**
+ * Retrieve k
+ *
+ * @return k
+
+ */
+ public double k()
+ {
+ return _k;
+ }
+
+ /**
+ * Retrieve Lambda
+ *
+ * @return Lambda
+ */
+
+ public double lambda()
+ {
+ return _lambda;
+ }
+
+ @Override public double[] support()
+ {
+ return new double[]
+ {
+ _k,
+ Double.POSITIVE_INFINITY
+ };
+ }
+
+ @Override public double density (
+ final double t)
+ throws Exception
+ {
+ if (!supported (
+ t
+ ))
+ {
+ throw new Exception (
+ "R1ParetoDistribution::density => Variate not in Range"
+ );
+ }
+
+ return _lambda * Math.pow (
+ _k,
+ _lambda
+ ) * Math.pow (
+ t,
+ -1. - _lambda
+ );
+ }
+
+ @Override public double cumulative (
+ final double t)
+ throws Exception
+ {
+ if (!supported (
+ t
+ ))
+ {
+ throw new Exception (
+ "R1ParetoDistribution::cumulative => Variate not in Range"
+ );
+ }
+
+ return 1. - Math.pow (
+ _k / t,
+ _lambda
+ );
+ }
+
+ @Override public double mean()
+ throws Exception
+ {
+ return _lambda * _k / (1. >= _lambda ? 1. - _lambda : _lambda - 1.);
+ }
+
+ @Override public double variance()
+ throws Exception
+ {
+ double mean = mean();
+
+ return _lambda * _k * _k / (2. >= _lambda ? 2. - _lambda : _lambda - 2.) - mean * mean;
+ }
+}
diff --git a/src/main/java/org/drip/measure/exponential/R1RateDistribution.java b/src/main/java/org/drip/measure/exponential/R1RateDistribution.java
index 714bd7d6f8c..07176176658 100644
--- a/src/main/java/org/drip/measure/exponential/R1RateDistribution.java
+++ b/src/main/java/org/drip/measure/exponential/R1RateDistribution.java
@@ -156,7 +156,7 @@ public R1RateDistribution (
final double lambda)
throws Exception
{
- if (!NumberUtil.IsValid (_lambda = lambda) || 0. > _lambda)
+ if (!NumberUtil.IsValid (_lambda = lambda) || 0. >= _lambda)
{
throw new Exception ("R1RateDistribution Constructor => Invalid lambda");
}
diff --git a/src/main/java/org/drip/measure/transform/GammaToR1Exponential.java b/src/main/java/org/drip/measure/transform/R1GammaToExponential.java
similarity index 97%
rename from src/main/java/org/drip/measure/transform/GammaToR1Exponential.java
rename to src/main/java/org/drip/measure/transform/R1GammaToExponential.java
index 399d87a520f..d9183f8addf 100644
--- a/src/main/java/org/drip/measure/transform/GammaToR1Exponential.java
+++ b/src/main/java/org/drip/measure/transform/R1GammaToExponential.java
@@ -82,7 +82,7 @@
*/
/**
- * GammaToR1Exponential implements the R1 Exponential Distribution in Terms of the
+ * R1GammaToExponential implements the R1 Exponential Distribution in Terms of the
* R1 Gamma Distribution. The References are:
*
*
@@ -119,12 +119,12 @@
* @author Lakshmi Krishnamurthy
*/
-public class GammaToR1Exponential
+public class R1GammaToExponential
extends R1ShapeScaleDistribution
{
/**
- * GammaToR1Exponential Constructor
+ * R1GammaToExponential Constructor
*
* @param scaleParameter Scale Parameter
* @param gammaEstimator Gamma Estimator
@@ -134,7 +134,7 @@ public class GammaToR1Exponential
* @throws Exception Thrown if the Inputs are Invalid
*/
- public GammaToR1Exponential (
+ public R1GammaToExponential (
final double scaleParameter,
final R1ToR1 gammaEstimator,
final R1ToR1 digammaEstimator,
diff --git a/src/main/java/org/drip/measure/transform/GammaToMaxwellBoltzmannSquared.java b/src/main/java/org/drip/measure/transform/R1GammaToMaxwellBoltzmannSquared.java
similarity index 96%
rename from src/main/java/org/drip/measure/transform/GammaToMaxwellBoltzmannSquared.java
rename to src/main/java/org/drip/measure/transform/R1GammaToMaxwellBoltzmannSquared.java
index 6c0c1419bfe..8926b637e58 100644
--- a/src/main/java/org/drip/measure/transform/GammaToMaxwellBoltzmannSquared.java
+++ b/src/main/java/org/drip/measure/transform/R1GammaToMaxwellBoltzmannSquared.java
@@ -82,7 +82,7 @@
*/
/**
- * GammaToMaxwellBoltzmannSquared implements the Maxwell-Boltzmann Squared Distribution using the
+ * R1GammaToMaxwellBoltzmannSquared implements the Maxwell-Boltzmann Squared Distribution using the
* R1 Gamma Distribution. The References are:
*
*
@@ -119,13 +119,13 @@
* @author Lakshmi Krishnamurthy
*/
-public class GammaToMaxwellBoltzmannSquared
+public class R1GammaToMaxwellBoltzmannSquared
extends R1ShapeScaleDistribution
{
private double _a = Double.NaN;
/**
- * GammaToMaxwellBoltzmannSquared Constructor
+ * R1GammaToMaxwellBoltzmannSquared Constructor
*
* @param a "A" Parameter
* @param gammaEstimator Gamma Estimator
@@ -135,7 +135,7 @@ public class GammaToMaxwellBoltzmannSquared
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
- public GammaToMaxwellBoltzmannSquared (
+ public R1GammaToMaxwellBoltzmannSquared (
final double a,
final R1ToR1 gammaEstimator,
final R1ToR1 digammaEstimator,
diff --git a/src/main/java/org/drip/sample/gammadistribution/MaxwellBoltzmannSquaredPDFEstimate.java b/src/main/java/org/drip/sample/gammadistribution/MaxwellBoltzmannSquaredPDFEstimate.java
index dc0cf9db095..0afbe82ba8b 100644
--- a/src/main/java/org/drip/sample/gammadistribution/MaxwellBoltzmannSquaredPDFEstimate.java
+++ b/src/main/java/org/drip/sample/gammadistribution/MaxwellBoltzmannSquaredPDFEstimate.java
@@ -3,7 +3,7 @@
import org.drip.function.definition.R1ToR1;
import org.drip.function.definition.R2ToR1;
-import org.drip.measure.transform.GammaToMaxwellBoltzmannSquared;
+import org.drip.measure.transform.R1GammaToMaxwellBoltzmannSquared;
import org.drip.service.common.FormatUtil;
import org.drip.service.env.EnvManager;
import org.drip.specialfunction.digamma.CumulativeSeriesEstimator;
@@ -239,8 +239,8 @@ public static final void main (
for (double a : aArray)
{
- GammaToMaxwellBoltzmannSquared maxwellBoltzmannSquaredDistribution =
- new GammaToMaxwellBoltzmannSquared (
+ R1GammaToMaxwellBoltzmannSquared maxwellBoltzmannSquaredDistribution =
+ new R1GammaToMaxwellBoltzmannSquared (
a,
gammaEstimator,
digammaEstimator,
@@ -281,8 +281,8 @@ public static final void main (
for (double a : aArray)
{
- GammaToMaxwellBoltzmannSquared maxwellBoltzmannSquaredDistribution =
- new GammaToMaxwellBoltzmannSquared (
+ R1GammaToMaxwellBoltzmannSquared maxwellBoltzmannSquaredDistribution =
+ new R1GammaToMaxwellBoltzmannSquared (
a,
gammaEstimator,
digammaEstimator,
@@ -321,8 +321,8 @@ public static final void main (
for (double a : aArray)
{
- GammaToMaxwellBoltzmannSquared maxwellBoltzmannSquaredDistribution =
- new GammaToMaxwellBoltzmannSquared (
+ R1GammaToMaxwellBoltzmannSquared maxwellBoltzmannSquaredDistribution =
+ new R1GammaToMaxwellBoltzmannSquared (
a,
gammaEstimator,
digammaEstimator,
diff --git a/src/main/java/org/drip/sample/pareto/R1CDFAndPDF.java b/src/main/java/org/drip/sample/pareto/R1CDFAndPDF.java
new file mode 100644
index 00000000000..f5f484520ea
--- /dev/null
+++ b/src/main/java/org/drip/sample/pareto/R1CDFAndPDF.java
@@ -0,0 +1,197 @@
+
+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;
+
+/*
+ * -*- 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.
+ */
+
+/**
+ * R1CDFAndPDF 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 R1CDFAndPDF
+{
+
+ /**
+ * 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 (Left-most Value)"
+ );
+
+ System.out.println (
+ "\t|| - Probability Density across Time Horizons (Right-most columns)"
+ );
+
+ System.out.println (
+ "\t||--------------------------------------------------------------------------------------------------------||"
+ );
+
+ for (int i = 0; i < lambdaArray.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)
+ {
+ metricDisplay += " " + FormatUtil.FormatDouble (
+ paretoDistribution.density (horizonArray[j]), 1, 6, 1.
+ ) + " |";
+ }
+
+ System.out.println (metricDisplay + "|");
+ }
+
+ System.out.println (
+ "\t||--------------------------------------------------------------------------------------------------------||"
+ );
+
+ System.out.println();
+
+ System.out.println();
+
+ EnvManager.TerminateEnv();
+ }
+}
diff --git a/src/main/java/org/drip/sample/pareto/package-info.java b/src/main/java/org/drip/sample/pareto/package-info.java
new file mode 100644
index 00000000000..0c04b82f2db
--- /dev/null
+++ b/src/main/java/org/drip/sample/pareto/package-info.java
@@ -0,0 +1,8 @@
+
+/**
+ * R1 Pareto Distribution Run Sweep
+ *
+ * @author Lakshmi Krishnamurthy
+ */
+
+package org.drip.sample.pareto;