Fitting power-law distributions with poweRlaw package in R

Question

With poweRlaw library, and once computed alpha and xmin with estimate_xmin, which formula the script uses to compute the fitted values? I mean, assuming that y=C·x^(-alpha), my question is how the script computes the normalization constant from alpha and xmin.

Answer 1

The normalising constant is fairly easy to calculate. See the Clauset et al's powerlaw paper (in particular table 2.1). For the continuous case, C = (alpha-1) xmin^(alpha-1), the discrete case involves calculating the diagamma function.

You can also examine the R code:

• Discrete
• Continuous