The Compound $F$ Distribution

Abstract

The $F$ distributions are becoming increasingly prominent in several applied areas. In this paper, a new generalization of the $F$ distribution is introduced by compounding. It takes the form of the product of two $F$ pdf's. Various structural properties of this distribution are derived, including its cdf, moments, mean deviation about the mean, mean deviation about the median, entropy, asymptotic distribution of the extreme order statistics, maximum likelihood estimates and the Fisher information matrix.