Approximations for discrete scan statistics on the circle

Discrete scan statistics are used for testing the null hypothesis that the observations are identically distributed against a clustering alternative that specifies an increased incidence of observations in a connected subregion of the circle. To implement the testing procedures based on the scan statistics, accurate approximations are needed for their tail probabilities. In this article we derive accurate product-type and Poisson-type approximations for the probabilities of discrete scan statistics for the binomial and the Poisson models. Numerical results are presented to evaluate the performance of the approximations derived in this article. (C) 1999 Elsevier Science B.V. All rights reserved.