Use of Coxian-Type Distributions in a General Model of the Maximum of Bivariate Random Variables

摘要

The paper extends an approach that uses trivariate reduction to model the maximum of bivariate random variables. Coxian-type phase distributions are used to define each element in the reduction because they are known to represent 'general' distributions and, therefore, lend a generality to the bivariate cases that can be modeled. Exact expressions for the moments and for the distribution function of the maximum are presented. Numerical examples demonstrate use of the model and provide some insights about the nature of the maximum.