Distribution of run statistics in partially exchangeable processes

Abstract

Let {X-i}(i >= 1) be an infinite sequence of recurrent partially exchangeable binary random variables. We study the exact distributions of two run statistics ( total number of success runs and the longest success run) in {X-i}(i >= 1). Since a flexible class of models for binary sequences can be obtained using the concept of partial exchangeability, as a special case of our results one can obtain the distribution of runs in ordinary Markov chains, exchangeable and independent sequences. The results also enable us to study the distribution of runs in particular urn models.