The necessary and sufficient conditions for dependent quadratic forms to be distributed as multivariate gamma

C. G. Khatri

Journal of Multivariate Analysis, 1980, vol. 10, issue 2, 233-242

Abstract: Let S be distributed as noncentral Wishart given by Wp(m, [Sigma], [Omega]) and let x be an n - 1 random vector distributed as N([mu], V). If qi = x'Aix + 2l'ix + ci, i = 1, 2,..., p, are p dependent second degree polynomials in the elements of x where Aj's are symmetric matrices, then the necessary and sufficient conditions for q1 , q2 ,..., qp to be distributed as the diagonal elements of S are established and this generalizes the result for [Sigma] = I. Some special cases are considered.

Keywords: Second; degree; polynomials; multivariate; normal; identically; distributed; eigenvalues; connected; structure (search for similar items in EconPapers)
Date: 1980
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