COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Post Office Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 865

"The Characteristic Function of the Dirichlet and Multivariate F Distributions"

Peter C.B. Phillips

January 1988

Formulae are derived for the characteristic function of the inverted Dirichlet distribution and hence the multivariate F. The analysis involves a new function with multiple arguments that extends the confluent hypergeometric function of the second kind. This function and its properties are studied in the paper and a simple integral representation is given which is useful for numerical work. A special case connected with the multivariate t distribution is also explored.

JEL Classification: 211

Keywords: Hypergeometric function, contour integral, differential equation, characteristic function