APPROXIMATIONS FOR THE TAIL PROBABILITIES AND MOMENTS OF THE SCAN STATISTIC

The scan statistic is used to test the hypothesis that the observed ev ents occur at random (uniformly distributed) in time or space versus t he hypothesis that they cluster within a moving window of size w. To i mplement the testing procedure based on the scan statistic its tail pr obabilities have to be effectively evaluated. In this article a survey of results on the approximations of the distribution of the scan stat istic and its moments is presented. Numerical results comparing these approximations are also given. Numerous references with applications i n epidemiological studies using the scan statistics are mentioned. Rel ated scan statistics that have been used in many other interesting app lications are listed in the reference section. The article concludes w ith the presentation of unsolved problems related to the scan statisti c.