Abstract
Scan statistics describe large number of events or objects clustered close in time or space. A few special cases of scan statistics – long success runs and the sample range – have been widely applied and their distributions known for hundreds of years. Most of the theory on the probability of scan statistics was developed after 1960. Prior to 1960, researchers in various fields have used scan statistics and were either limited to the special cases or used rough distributional approximations. In some cases, they did not fully take into account in their likelihood analysis the overlapping scanning nature of how they selected clusters.For the continuous case, the times when (or locations where) events can occur can be anywhere within an interval (or region). For the discrete case, the events can occur anywhere on a grid, a special case being a sequence of Bernoulli trials. We separate the history for the discrete and continuous cases because they grew out of different applications.