A series of Matlab functions for fitting various forms of power-law distributions to data using maximum likelihood estimation. All of these functions are actual maximum likelihood estimates. If you are using small sample size data you should consider using the minimum variance unbiased estimators. These functions were published as a supplement to White et al. 2008 and are linked directly to these published files. Use of this software should be acknowledged by citation of the original paper.

Primary developer & maintainer: Ethan White

Other significant contributors: Jessica Green

Pareto Distribution

Estimates the exponent for the Pareto Distribution (xmin<x<inf, exponent<-1) based on a vector of observations (data) and the minimum attainable value of x (xmin). Download the m file

Power Function Distribution

Estimates the exponent for the "Power Function Distribution" (sensu Evans et al. 2000; 0<x<xmax, exponent>-1) based on a vector of observations (data) and the maximum attainable value of x (xmax). There is an error in the MLE solution presented by Evans et al. 2000. The corrected form of the equation is presented in White et al. 2008 and utilized in this function. Download the m file

Truncated Pareto Distribution

Estimates the exponent for truncated Pareto data when provided with the minimum attainable value of x (xmin), the maximum atttainable value of x (xmax), and a vector of observations (data). The function mle_pareto must also be accessible by Matlab (i.e., in the path or in the current directory) to allow for the calculation of a starting point for the numerical solution. Download the m file

Discrete Pareto Distribution

Estimates the exponent for the discrete Pareto (a power law distribution where only integer values are possible) when provided with the a vector of observations (data). This function fits the special case where the minimum attainable value, a, is equal to 1 as would be the case for most ecological data, and assumes an infinite maximum value. Download m file