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Advances in computation of the maximum of a set of random variables

This paper quantifies the approximation error in Clark's approach presented in C. E. Clark (1961) to computing the maximum (max) of Gaussian random variables; a fundamental operation in statistical timing. We show that a finite look up table can be used to store these errors. Based on the error computations, approaches to different orderings for pair-wise max operations on a set of Gaussians are proposed. Experiments show accuracy improvements in the computation of the max of multiple Gaussians by up to 50% in comparison to the traditional approach. To the best of our knowledge, this is the first work addressing the mentioned issues