Analysis of Heavy Tailed Distributions.
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.