Talk:Generalized Gaussian distribution

Merger proposal

This is the same distribution as Generalized normal distribution. While it shouldn't be too hard to merge the two, the main question is which name to use? Any comments? -3mta3 (talk) 12:46, 2 March 2009 (UTC)

One thing that needs thinking about is how to handle other distributions which are also called "generalised normal". For example, documentaion for R includes a generalised normal distribution which is not the one referred to here (see eg. [1] ). Nether of these distributions is what is called either the skew-generalised normal or skew-normal distribution. Also I note that the ISI glossary has "Kapteyn's univariate distribution" as an alternative name for a generalised normal (not clear which) [2], but I guess this name should be avoided. Melcombe (talk) 14:31, 2 March 2009 (UTC)

I agree. I added this page recently because I didn't find this distribution (under either name) on the List of probability distributions page. Since "Gaussian distribution" redirects to "Normal distribution", I propose that we merge these two pages under "generalized normal distribution" with a redirect from "generalized Gaussian distribution." Then we can add a comment in the text about the "Kapteyn" name. I don't know what to do about the other generalized normal distribution. Maybe we could have them on the same page with two copies of the probability distribution template. Skbkekas (talk) 16:39, 2 March 2009 (UTC)

On further investigation, the generalized normal distribution referred to in the R documentation cited above ([3]) does not appear to include the normal distribution as a special case (also, the literature reference in the R code is to a 1990 paper of Hosking's, but this paper does not discuss anything like the distribution in the R code, and I didn't find any use of the term "generalized normal" in Hosking's other papers on JSTOR). In that sense, it is "generalized" in the same way that the lognormal, inverse normal, and half-normal distributions are (i.e. derived from the normal via a transformation). I think we can clarify that "generalized here" means a parameteric family that includes the normal distribution as a special case. This includes skew-normal, which already has a page that we can link to. Skbkekas (talk) 19:22, 2 March 2009 (UTC)