Discrete, continuous and conditional multiple window scan statistics

Abstract

The distributions of discrete, continuous and conditional multiple window scan statistics are studied. The finite Markov chain imbedding technique has been applied to obtain the distributions of fixed window scan statistics defined from a sequence of Bernoulli trials. In this manuscript the technique is extended to compute the distributions of multiple window scan statistics and the exact powers for multiple pulse and Markov dependent alternatives. An application in blood component quality monitoring is provided. Numerical results are also given to illustrate our theoretical results.