The Greatest of a Finite Set of Random Variables
Charles Edward Clark · Operations Research · 1961
The variables ξ1, …, ξn have a joint normal distribution. We are concerned with the calculation or approximation of max(ξ1, …, ξn). Current analyses and tables handle the case in which the ξı 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.