A Special Distributional Result for Bilinear Forms.

摘要

Necessary and sufficient conditions are given such that a quadratic form has moment generating function E = (1-t-squared) -r/4 power for abs. val. t < 1 with U approx. N sub k (mu, Sigma) and Sigma positive definite. An important corrollary gives conditions under which the bilinear form X'AY involving two different multivariate normal random vectors (of not necessarily the same dimensions) has the same distribution as the sum of independent random variables, each having the LaPlace (double exponential) distribution. (Author)