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Biometrika 1988 75(4):715-722; doi:10.1093/biomet/75.4.715
© 1988 by Biometrika Trust
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A double sequential procedure for detecting a change in distribution

DAVID ASSAF and YAAKOV RITOV

Department of Statistics, Hebrew University of Jerusalem Jerusalem, Israel 91905

Let X1, X2,... be such that X1,... XT–1, have the distribution F0, while XT, XT+1,... have the distribution F1. Think of X1, X2,... as samples from large batches and suppose T has a prior geometric distribution. Sampling from each batch is assumed to give rise to a Brownian motion process and we are interested in both an optimal sampling scheme and an optimal stopping time to detect the changepoint T. The suggested procedure may roughly be described as a sequence of sequential probability ratio tests. A comparison of our procedure with the fixed size sampling procedure, with the same level of false alarms and the same average sample size per batch, shows that our procedure is significantly superior in that it detects the changepoint much faster.

Key Words: Brownian motion • Probability of false alarm • Sequential probability ratio test


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