I'm new to this group, so my question may have been answered earlier.
Suppose we know all marginal distributions of n random variables.
There are of
course in general many joint distributions which have these marginal
distributions, (We may for instance multiply the marginal
distributions if we assume independence.) I want to narrow down the
choice by specifying all
covariances. It is easy to see that I cannot choose any set of
covariances even if I secure that the variance/covariance matrix to be
positive semidefinite. Is there a set of conditions on the covariances
which guarantees that a joint distribution exists?
.
.
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