PowerLaws.jl

Specification of discrete and continuous power-law distributions according to Distributions.jl. This package is implemented according to POWER-LAW DISTRIBUTIONS IN EMPIRICAL DATA

This is a maintained fork of the archive PowerLaws.jl. Currently, the functionality replicates the original package, but with some compatibility upgrades, and modernised package structure. This will probably change in the future. Braking changes are however introduced by renaming structs and functions:

• powerlaw_con -> ContinuousPowerLaw
• powerlaw_dis -> DiscretePowerLaw
• estimate_xmin -> estimate_parameters
• compare_distributions -> DistributionComparison

Installation

This package is not (yet) registered, but can be installed with the following command:

using Pkg
Pkg.add(url="https://www.github.com/TimVWese/PowerLaws.jl")

Functionality

Discrete Power-Law Distribution

DiscretePowerLaw(α, θ) represents a discrete power-law distribution with negative exponent α and minimum value θ. The probability mass function is given by

$p(x) = \\begin{cases} \\frac{x^{-\\alpha}}{\\zeta(\\alpha, \\theta)} & x \\geq \\theta \\\\ 0 & x < \\theta \\end{cases}$

Continuous Power-Law Distribution

ContinuousPowerLaw(α, θ) represents a continuous power-law distribution with negative exponent α and minimum value θ. The probability density function is given by

$p(x) = \\begin{cases} \\frac{(\\alpha - 1)}{\\theta} \\left(\\frac{x}{\\theta}\\right)^{-\\alpha} & x \\geq \\theta \\\\ 0 & x < \\theta \\end{cases}$

Inpired by python powerlaw package and R poweRlaw package