Abstract
Let ( X 1, X 2,…, X q ) have the multivariate dirichlet distribution with parameters ( p 1, p 2,…, p q ), on the linear space of symmetric ( r, r) real matrices. We prove that for a given set of positive numbers f 1, f 2,…, f q one has E[(det(f 1X 1+…+f qX q)) −(p1+…+pq)]=f −rp1 1…f −rp1 q . This extends a useful formula already known in dimension r = 1.
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