In this paper, we study the distributions of the number of success runs of length k and the number of success runs of length k given the number of successes in a sequence of independent and identically distributed (i.i.d.) binary trials arranged on a circle (circular sequence) based on three...

Let X1, X2,...,Xn be a time-homogeneous {0, 1}-valued Markov chain. Let Y = (Y1,...,Yr) denote the r-dimensional random vector, where Yi(i = l,...,r) represents the number of success runs of length ki(i = 1,...,r), k = (kl,...,kr). In this paper we obtain exact and recurrence formulae for the...

The exact distribution of the number of occurrences of subpattern of a specified length or larger until the first occurrence of a pattern is studied in a sequence of multi-state independent trials. If the pattern and the subpattern of the specified lengths, respectively, satisfy a condition and...