Hypergeometric Functions of Many Matrix Variables and Distributions of Generalized Quadratic Forms

SYNOPTIC ABSTRACT

A representation of the exact density of a linear function of independent matrix-variate gamma variables, in terms of hypergeometric function of many matrix variables, is considered. The result is obtained in terms of a φ₂ function of many matrix variables. Connection of the linear function to generalized quadratic forms is pointed out. The exact moments and the exact density of the determinant of such a linear combination are also derived.

Key Words and Phrases:

• Matrix-variate gamma
• linear functions
• φ₂ function of many matrix variables
• generalized quadratic form
• determinant of a linear function
• exact density
• exact moments