The Greatest of a Finite Set of Random Variables

Charles E. Clark
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Charles E. Clark: System Development Corporation, Santa Monica, California

Operations Research, 1961, vol. 9, issue 2, 145-162

Abstract: The variables (xi) 1 , ..., (xi) n have a joint normal distribution. We are concerned with the calculation or approximation of max((xi) 1 , ..., (xi) n ). Current analyses and tables handle the case in which the (xi) 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.

Date: 1961
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