Statistica Sinica

Katuomi Hirano and Sigeo Aki

Abstract:LetX_{1},X_{2}, ...,X_{n}be a time-homogeneous {0,1}-valued Markov chain. The probability distribution of number of runs of ``1'' of length at leastkin the sequenceX_{1},X_{2}, ...,X_{n}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 lengthkin 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 orderk, sequence matching.