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Approximations and Inequalities for Moving Sums

Joseph Glaz (), Joseph Naus () and Xiao Wang ()
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Joseph Glaz: University of Connecticut
Joseph Naus: The State University of New Jersey
Xiao Wang: University of Connecticut

Methodology and Computing in Applied Probability, 2012, vol. 14, issue 3, 597-616

Abstract: Abstract In this article accurate approximations and inequalities are derived for the distribution, expected stopping time and variance of the stopping time associated with moving sums of independent and identically distributed continuous random variables. Numerical results for a scan statistic based on a sequence of moving sums are presented for a normal distribution model, for both known and unknown mean and variance. The new R algorithms for the multivariate normal and t distributions established by Genz et al. (2010) provide readily available numerical values of the bounds and approximations.

Keywords: Approximation; Moving sum; Multivariate normal; Multivariate T; Probability inequality; R algorithms; Scan statistics; Stopping time; 60E15; 60G10; 62E17; 62M07 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s11009-011-9251-x

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