A Special Distributional Result for Bilinear Forms
给出了二次型矩母函数为特定形式的充要条件，并推导出两个不同多元正态随机向量的双线性形式可表示为独立拉普拉斯随机变量之和的条件。
Abstract Necessary and sufficient conditions are given such that a quadratic form has moment-generating function E[exp ( tU′BU)] = (1 – t 2)–r/4 for |t| < 1 with U ∼ Nk (μ, Σ) and Σ positive definite. An important corollary 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.