|Date: ||Fri, 5 Jan 2001 09:00:38 -0500|
|Sender: ||"SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>|
|Subject: ||Re: Generating Nonnormal Data|
|Content-type: ||text/plain; charset=us-ascii|
> Probability distributions are not uniquely determined by their first
> four moments so there is no unique way to select a probability
> distribution given the skew and kurtosis.
I would think that, in addition to the first four moments, one could come
up with a fifth
condition which would uniquely determine such a distribution. You might
have to come up
with a definition of "mathematically most simple continuous distribution"
most simple continuous distribution" to achieve this.
> However, depending on your objectives, you may be able to solve your
problem by selecting
> from a family of distributions that are uniquely determined by their
> four moments.