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The poweRlaw package

This package implements both the discrete and continuous maximum likelihood estimators for fitting the power-law distribution to data using the methods described in Clauset et al, 2009. It also provides function to fit log-normal and Poisson distributions. Additionally, a goodness-of-fit based approach is used to estimate the lower cut-off for the scaling region.

The code developed in this package was influenced from the python and R code found at Aaron Clauset’s website. In particular, the R code of Laurent Dubroca and Cosma Shalizi.

To cite this package in academic work, please use:

Gillespie, C. S. “Fitting heavy tailed distributions: the poweRlaw package.” Journal of Statistical Software, 64(2) 2015. (pdf).

For a different way of handling powerlaw type distributions, see

Gillespie, C.S. ” Estimating the number of casualties in the American Indian war: a Bayesian analysis using the power law distribution.” Annals of Applied Statistics, 2017. (pdf)

Installation

This package is hosted on CRAN and can be installed in the usual way:

install.packages("poweRlaw")

Alternatively, the development version can be install from from github using the devtools package:

install.packages("devtools")
devtools::install_github("csgillespie/poweRlaw")

Getting Started

To get started, load the package

library("poweRlaw")

then work through the four vignettes (links to the current CRAN version):

Alternatively, you can access the vignettes from within the package:

browseVignettes("poweRlaw")

The plots below show the line of best fit to the Moby Dick and blackout data sets (from Clauset et al, 2009).

Other information

  • If you have any suggestions or find bugs, please use the github issue tracker
  • Feel free to submit pull requests
  • Data was originally obtained from Arron Clausett’s website. But this site is no longer available.

Development of this package was supported by Jumping Rivers

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Install

install.packages('poweRlaw')

Monthly Downloads

5,307

Version

0.80.0

License

GPL-2 | GPL-3

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Last Published

January 25th, 2024

Functions in poweRlaw (0.80.0)

population

City boundaries and the universality of scaling laws
poweRlaw-package

The poweRlaw package
lines,distribution-method

Generic plotting functions
get_ntail

Values greater than or equal to xmin
moby

Moby Dick word count
swiss_prot

Word frequency in the Swiss-Prot database
show,distribution-method

Generic show method for distribution objects
dpldis

Discrete power-law distribution
dist_pdf

The probability density function (pdf)
dist_all_cdf

The data cumulative distribution function
dist_cdf

The cumulative distribution function (cdf)
bootstrap_moby

Example bootstrap results for the full Moby Dick data set
dist_rand

Random number generation for the distribution objects
dplcon

The continuous power-law distribution
compare_distributions

Vuong's test for non-nested models
dist_ll

The log-likelihood function
conlnorm-class

Heavy-tailed distributions
estimate_pars

Estimates the distributions using mle.
get_KS_statistic

Deprecated function
get_bootstrap_sims

Estimating the lower bound (xmin)
plot.bs_xmin

Plot methods for bootstrap objects
native_american

Casualties in the American Indian Wars (1776 and 1890)
get_n

Sample size