Open Access
May, 1991 Tight Bounds and Approximations for Scan Statistic Probabilities for Discrete Data
Joseph Glaz, Joseph I. Naus
Ann. Appl. Probab. 1(2): 306-318 (May, 1991). DOI: 10.1214/aoap/1177005940

Abstract

Let X1,X2, be a sequence of independently and identically distributed integer-valued random variables. Let Ytm+1,t for t=m,m+1, denote a moving sum of m consecutive Xi's. Let Nm,T=maxmtT{Ytm+1,t} and let τk,m be the waiting time until the moving sum of Xi's in a scanning window of m trials is as large as k. We derive tight bounds for the equivalent probabilities P(τk,m>T)=P(Nm,T<k). We apply the bounds for two problems in molecular biology: the distribution of the length of the longest almost-matching subsequence in aligned amino acid sequences and the distribution of the largest net charge within any m consecutive positions in a charged alphabet string.

Citation

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Joseph Glaz. Joseph I. Naus. "Tight Bounds and Approximations for Scan Statistic Probabilities for Discrete Data." Ann. Appl. Probab. 1 (2) 306 - 318, May, 1991. https://doi.org/10.1214/aoap/1177005940

Information

Published: May, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0738.60039
MathSciNet: MR1102323
Digital Object Identifier: 10.1214/aoap/1177005940

Subjects:
Primary: 60F10
Secondary: 60F99

Keywords: clustering probabilities , Longest matching subsequences , scan statistics

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.1 • No. 2 • May, 1991
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