Parameters in Frechet distribution


I am using brms to model some data with the Frechet family. According to the doc for the Frechet family the parameters mu and nu are estimated (2 parameters). However, the Frechet distribution is often formulated with 3 parameters, location, scale, and shape, which is also the case for the function dfrechet(x, loc = 0, scale = 1, shape = 1, log = FALSE) included in bmrs ( How does nu relate to the scale and shape of this distribution? I would like to get the estimated PDF from the parameters in the posterior.


  • Operating System: Win 10
  • brms Version: 2.13.0

I think this has the info on how to go from scale/nu to mu/nu:

oh right, I missed that page. So given mu (location) and nu (shape) I get s <- mu/gamma(1-1/nu) (scale) and so I have the 3 parameters I need. Thank you for pointing me in the right direction

EDIT: Correction. brms estimated mu as the mean of the distribution. This is not the location parameter as I wrongly suggested before. The location parameter in set to 0. So to generate PDFs from the posterior distribution you should use dfrechet(x, loc = 0, scale = nu, shape = mu/gamma(1-1/nu)).

Correction: dfrechet(x, loc = 0, scale = mu / gamma(1 - 1 / nu), shape = nu)