1 results
Distribution of the scan statistic for a sequence of bistate trials
- Part of
-
- Journal:
- Journal of Applied Probability / Volume 38 / Issue 4 / December 2001
- Published online by Cambridge University Press:
- 14 July 2016, pp. 908-916
- Print publication:
- December 2001
-
- Article
- Export citation
-
Let
be the scan statistic of window size r for a sequence of n bistate trials 
. The scan statistic Sn(r) has been successfully used in various fields of applied probability and statistics, and its distribution has been studied extensively in the literature. Currently, all existing formulae for the distribution of Sn(r) are rather complex, and they can only be numerically implemented when is a sequence of Bernoulli trials, the window size r is less than 20 and the length of the sequence n is not too large. Hence, these formulae have been limiting the practical applications of the scan statistic. In this article, we derive a simple and effective formula for the distribution of Sn(r) via the finite Markov chain embedding technique to overcome some of the limitations of the existing complex formulae. This new formula can be applied when is either a sequence of Bernoulli trials or a sequence of Markov dependent bistate trials. Selected numerical examples are given to illustrate our results.
be the scan statistic of window size 
. The scan statistic 