Approximations and Inequalities for Moving Sums

Joseph Glaz, Joseph Naus, Xiao Wang

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)597-616
Number of pages20
JournalMethodology and Computing in Applied Probability
Issue number3
StatePublished - Sep 2012

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)


  • Approximation
  • Moving sum
  • Multivariate T
  • Multivariate normal
  • Probability inequality
  • R algorithms
  • Scan statistics
  • Stopping time

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