Parametrization of continuous univariate distributions

[jpeyhardi]

There exists two parametrizations of the Gamma distribution : see https://en.wikipedia.org/wiki/Gamma_distribution
One with a shape and scale parameters and the other with a shape and rate parameters.
In order to be more comparable with other distributions defined in StatisKit.Core, I propose to use the first definition.
More generally should not we propose a location and a scale parameter for all continuous univariate distributions ?
It is always possible to define the cdf $F_{u,s}(x):=F((x-u)/s)$.
The advantage would be to obtain more comparable distributions.

[pfernique]

Possibly, but keep in mind that estimation algorithms should be modified accordingly.

[pfernique]

And is it consistent with Gamma GLMs ?

[jpeyhardi]

It seems that the Gamma has been described with a third parametrization in the GLM framework; see the book "Genralized Linear Models" of McCullagh and Nelder (1989).
Nevertheless, this third parametrization uses the scale parameter and use the inverse of the shape parameter k (used in the wikipedia version 1).