Package org.drip.measure.continuous

Class R1PowerLawDistribution

java.lang.Object

org.drip.measure.continuous.R1Distribution

org.drip.measure.continuous.R1PowerLawDistribution

public abstract class R1PowerLawDistribution
extends R1Distribution

R1PowerLawDistribution implements the R¹ Power Law 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 4^th 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

It provides the following Functionality:

• Retrieve Power Law "k"
• Retrieve Lambda

Module	Computational Core Module
Library	Numerical Analysis Library
Project	Rd Continuous/Discrete Probability Measures
Package	R1 and Rd Continuous Random Measure

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
R1PowerLawDistribution()

Method Summary

Modifier and Type	Method	Description
double	k()	Retrieve Power Law "k"
double	lambda()	Retrieve Lambda

Methods inherited from class org.drip.measure.continuous.R1Distribution

bPOE, centralMoment, cumulative, cvar, density, differentialEntropy, excessKurtosis, expectedShortfall, fisherInformation, histogram, incremental, invCumulative, iqr, kullbackLeiblerDivergence, mean, median, mode, momentGeneratingFunction, nonCentralMoment, populationCentralMeasures, probabilityGeneratingFunction, quantile, random, randomArray, skewness, support, supported, tukeyAnomaly, tukeyCriterion, variance

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

R1PowerLawDistribution

public R1PowerLawDistribution()

Method Details

k

public double k()

Retrieve Power Law "k"

Returns:

The Power Law "k"

lambda

public double lambda()

Retrieve Lambda

Returns:

Lambda