Published online by Cambridge University Press: 14 July 2016
Let {X i }i=1 n be a sequence of random variables with two possible outcomes, denoted 0 and 1. Define a random variable S n,m to be the maximum number of 1s within any m consecutive trials in {X i }i=1 n . The random variable S n,m is called a discrete scan statistic and has applications in many areas. In this paper we evaluate the distribution of discrete scan statistics when {X i }i=1 n consists of exchangeable binary trials. We provide simple closed-form expressions for both conditional and unconditional distributions of S n,m for 2m ≥ n. These results are also new for independent, identically distributed Bernoulli trials, which are a special case of exchangeable trials.