On the distribution of a random matrix

Abstract

Let Y₁ and Y₂ be distributed as independent normal p-vectors with the means respectively and with the same covariance matrix Σ and let S be distributed as Wishart W_p (N₁+N₂ −2,Σ), independent of Y₁ and Y₂. In this paper an analytic derivation of the distribution of the 2×2 matrix M=Y'S⁻¹ γ where Y = (Y₁, Y₂) and μ and ν are arbitrary vectors is given, following the same lines of derivation as in Sitgreaves (1952).

Keywords:

• normal distribution
• Wishart distribution
• classification problems