Re: [Rd] p-generalized normal distribution

From: Steve Kalke <steve.kalke_at_uni-rostock.de>
Date: Tue, 01 Dec 2009 18:08:09 +0100

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 θ-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 ...)
>
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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)).



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