From steve.kalke at uni-rostock.de  Tue Dec  1 18:08:09 2009
From: steve.kalke at uni-rostock.de (Steve Kalke)
Date: Tue, 1 Dec 2009 18:08:09 +0100
Subject: [Rd] p-generalized normal distribution
In-Reply-To: <loom.20091128T024128-643@post.gmane.org>
References: <4B0C0FA2.2020104@uni-rostock.de>
	<loom.20091128T024128-643@post.gmane.org>
Message-ID: <4B154D79.9060501@uni-rostock.de>

Ben Bolker schrieb:
> Steve Kalke <steve.kalke <at> uni-rostock.de> writes:
>
>   
>> I would like to know if there is an R-package available for 
>> computing the density, distribution function,
>> quantiles and random 
>> numbers of the p-generalized normal distribution or 
>> if somebody is already working on it.
>>     
>
>   I haven't been able to find out what the p-generalized normal
> distribution is: the only paper I can find is
>
> Sinz, F., and M. Bethge$. 2009. Characterization of the p-generalized 
> normal distribution. Journal of Multivariate Analysis 100:817-820. 
> doi: 10.1016/j.jmva.2008.07.006.
>
> and I don't have access to it at the moment (although it does
> at least hint that the required distribution is multivariate;
> maybe p-dimensional?).  
>
>  Is it the same as this?
>
> Goodman, I. R., and S. Kotz. 1973. Multivariate ?-generalized normal
> distributions. Journal of Multivariate Analysis 3:204-219. doi:
> 10.1016/0047-259X(73)90023-7.
>
>   Where can we find a description?
>
>   (Short answer: as far as I can tell, it doesn't exist in
> R, but it would be good to have more information ...)
>
> ______________________________________________
> R-devel at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-devel
>   

The p-generalized normal distribution was introduced in M.T. Subbotin's 
"On the law of frequency of errors" (1923), later studied in e.g. 
"Distributions in Statistics-Continous Univariate Distributions-2" from 
Johnson and Kotz (1970) or in "Continous l_n,p-symmetric distributions" 
from W.-D. Richter (2009), Lithuanian Math. J. 49.

A vector X=(X_1,...,X_n) is said to be p-generalized nomal distributed, 
if it's density function satisfies the reprensentation  f(x)=C^n * exp[-( 
|x_1|^p+...+|x_n|^p ) / p ] with C=p^(1-1/p)/(2*GAMMA(1/p)).



[Rd] p-generalized normal distribution
Steve Kalke