Statistica Sinica 3(1993), 313-320

ON NUMBER OF OCCURRENCES OF

SUCCESS RUNS OF SPECIFIED LENGTH

IN A TWO-STATE MARKOV CHAIN

Katuomi Hirano and Sigeo Aki

The Institute of Statistical Mathematics and Osaka University

Abstract: Let X1X2, ...,  Xn be a time-homogeneous {0,1}-valued Markov chain. The probability distribution of number of runs of ``1'' of length at least k in the sequence X1X2, ..., Xn is studied. The probability generating function and some characteristics of the distribution are given in a simple form. Another distribution of number of runs of ``1'' of length k in the sequence by a different way of counting is also investigated.

Key words and phrases: Probability generating function, discrete distributions, Markov chain, binomial distribution of order k, sequence matching.