Exact distribution of the max/min of two Gaussian random variables

Authors:
Saralees Nadarajah;Samuel Kotz
Affiliations:
University of Manchester, Manchester, UK;George Washington University, Washington, DC
Venue:
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Year:
2008

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Abstract

Maximum and minimum of correlated Gaussian random variables arise naturally with respect to statistical static time analysis. It appears, however, that only approximations have been used in the recent literature to study the distribution of the max/min of correlated Gaussian random variables. In this paper, we would like to point out that the statistics literature has long established simple expressions for the exact distribution of the max/min. We provide some of the known expressions for the following: the probability density function, moment generating function, and the moments. We also provide two simple programs for computing the probability density functions of the max/min and an illustration of the results to statistical static time analysis.