Ben Bolker schrieb:
Steve Kalke 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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