Distribution of waiting time until the rth occurrence of a compound pattern

In this article, we investigate the waiting time distributions for the rth (r⩾1) occurrence of a compound pattern with respect to nonoverlapping and overlapping counting schemes in a sequence of Markov dependent multistate trials. Based on the finite Markov chain imbedding approach, the exact distribution, mean, variance and probability generating function are obtained. In addition, an alternative way of finding the probability generating function is presented.