Approximations for Multiple Scan Statistics on the Circle

Multiple scan statistic is usually used by epidemiologist to test the uniformity or clustering of data. In this article, we extend the work of Lin (1999) to give a general expression for the moments of multiple scan statistic on a circle, and use these moments to approximate its distribution using Markov chain and compound Poisson approximations proposed by Huffer and Lin (1997a) and Lin (1993). Numerical results are presented to evaluate the performance of these approximations.