In article <[EMAIL PROTECTED]>,
Hideo HIROSE <[EMAIL PROTECTED]> wrote:
>Are there any random number generation schemes for the generalized
>gaussian distribution:
>density g(x)=c*exp(-0.5*|x|^beta)
It is a little easier to do this with the "0.5" removed.
The distribution is symmetric, so it is sufficient to
do it on (0,infinity) and add a random sign.
If beta >= 1, this can be done easily. Let U be a
uniform (0,1) random variable; if U < 1 - 1/beta,
set X = U, f = 0. Otherwise, set f = E, an
exponential random variable with mean 1, and
set X = 1 + (E-1)/beta. Let T be a test exponential
random variable, and accept X if T+f - X^beta >= 0.
If one accepts, T may be reused.
If beta < 1, set X^beta = Y. Then Y has a Gamma
distribution with parameter 1/beta, and one can
use the methods for that.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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