Re: joint distribution of correlated uniform

From: Herman Rubin (hrubin_at_odds.stat.purdue.edu)
Date: 08/21/04 

Date: 21 Aug 2004 08:25:49 -0500

In article <tzb0eoc72euz@legacy>, Yan Xie <yxie2@uky.edu> wrote:
>Hello, all,

>1. Is it possible to get the joint distribution of n correlated
>uniform(0,1) random variables given the correlation matrix? If yes,
>any suggestion for it?
>2. Dose anybody have or happen to know an algorithm to generate
>positive definite matrix?
>Thanks in advance.

It is not possible even for normal unless it is assumed
that they are jointly normal; there is a "natural"
multivariate normal distribution which can be
characterized in many ways, one being that every linear
combination is normal.

As the normal distribution is the only nontrivial one
with a finite variance for which the distribution of
the sum of two independent random variables with that
distribution has a distribution of the same form, a
natural generalization to uniform does not exist. 

-- 
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, Department of Statistics, Purdue University
hrubin@stat.purdue.edu         Phone: (765)494-6054   FAX: (765)494-0558

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