Approximations for the tail probabilities and moments of the scan statistic

The scan statistic is used to test the hypothesis that the observed events occur at random (uniformly distributed) in time or space versus the hypothesis that they cluster within a moving window of size w. To implement the testing procedure based on the scan statistic its tail probabilities have to be effectively evaluated. In this article a survey of results on the approximations of the distribution of the scan statistic and its moments is presented. Numerical results comparing these approximations are also given. Numerous references with applications in epidemiological studies using the scan statistics are mentioned. Related scan statistics that have been used in many other interesting applications are listed in the reference section. The article concludes with the presentation of unsolved problems related to the scan statistic.