WAITING TIME DISTRIBUTIONS ASSOCIATED WITH RUNS OF FIXED LENGTH IN TWO-STATE MARKOV CHAINS

M. V. KOUTRAS

Department of Mathematics, University of Athens, Panepistemiopolis, 15784, Greece

(Received September 18, 1995; revised February 6, 1996)

Abstract. In the present article a general technique is developed for the evaluation of the exact distribution in a wide class of waiting time problems. As an application the waiting time for the r-th appearance of success runs of specified length in a sequence of outcomes evolving from a first order twostate Markov chain is systematically investigated and asymptotic results are established. Several extensions and generalisations are also discussed.

Key words and phrases: Waiting time distributions, success runs, distributions of order k, negative binomial distributions.