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StatisKit / Core

A Collection of Basic Utilities for Statistical Analyses
http://statiskit-core.rtfd.io/
Apache License 2.0
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Parametrization of continuous univariate distributions #79

Open jpeyhardi opened 5 years ago

jpeyhardi commented 5 years ago

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 commented 5 years ago

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

pfernique commented 5 years ago

And is it consistent with Gamma GLMs ?

jpeyhardi commented 5 years ago

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).