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Boundary crossing for moving sums

Published online by Cambridge University Press:  14 July 2016

J. Glaz  and
B. Johnson
J. Glaz*
Affiliation:
University of Connecticut
B. Johnson
Affiliation:
University of Connecticut
*
∗ Postal address: Department of Statistics, U-120. 196 Auditorium Road. University of Connecticut, Storrs, CT 06268. USA.
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Abstract

Let Xi, i ≧ 1, be a sequence of independent N(0, 1) random variables and Sj,m = Xj + · ·· + Xj+m–1, the jth moving sum. Let τ m = inf{j ≧ 1 : Sj,m > a} + m – 1, the boundary crossing time. Approximation in the spirit of Glaz and Johnson (1984), (1986) and Samuel-Cahn (1983) are given for Pr(τm > n), E(τ m), and σ (τ m),the standard deviation of τm.

Keywords

APPROXIMATIONSBOUNDARY CROSSING PROBABILITIESSHIFT DETECTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 1 , March 1988 , pp. 81 - 88
Copyright
Copyright © Applied Probability Trust 1988 

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Footnotes

†

Regrettably, Professor Johnson died on 4 November 1986.

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