Exact Distribution of the Max/Min of Two Gaussian Random Variables

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 literature to study the distribution of the max/min of correlated Gaussian random variables. In this paper...

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Bibliographic Details
Published in:IEEE transactions on very large scale integration (VLSI) systems 2008-02, Vol.16 (2), p.210-212
Main Authors: Nadarajah, S., Kotz, S.
Format: Article
Language:English
Subjects:
Applied sciences
Approximation
Correlation analysis
Distribution functions
Electric, optical and optoelectronic circuits
Electronics
Exact sciences and technology
Gaussian
Gaussian distribution
Mathematical analysis
Maximum
minimum
moment generating function (MGF)
moments
Probability density function
probability density function (pdf)
Probability density functions
Random variables
Statistical distributions
statistical static time analysis (SSTA)
Statistics
Theoretical study. Circuits analysis and design
Very large scale integration
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Summary: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 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.
ISSN:1063-8210
1557-9999
DOI:10.1109/TVLSI.2007.912191