The Greatest of a Finite Set of Random Variables

Abstract

The variables ξ 1 , …, ξ n have a joint normal distribution. We are concerned with the calculation or approximation of max(ξ 1 , …, ξ n ). Current analyses and tables handle the case in which the ξ ı are independently distributed with common expected values and common variances. This paper presents formulas and tables for the most general case with n = 2. When n > 2, the problem becomes cumbersome. This paper presents formulas and tables that permit approximations to the moments in case n > 2. The moments are approximated by iteration of a three-parameter computation or, alternatively, through successive use of a three-parameter table, which is given. Recent applications of the theory are described.