# What are the distributions on the positive k-dimensional quadrant with parametrizable covariance matrix? (bis)

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Wondering about the question I posted on Friday (on StackExchange, no satisfactory answer so far!), I looked further at the special case of the gamma distribution I suggested at the end. Starting from the moment conditions,

and

the solution is (hopefully) given by the system

The resolution of this system obviously imposes conditions on those moments, like

To

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