Bound on Poisson approximation on the length of success runs at least k by Stein-Chen method

Abstract

The probability distribution of the number of success runs of the length k (k ≥ 1) in n (n ≥ 1) Bernoulli trials is obtained. It is noted that this distribution is a binomial distribution of the order k, and several open problems pertaining to it are stated. Let Wn denotes the number of success runs with the length k or more and we give bound for Wn by Poisson distribution via Stein-Chen coupling method. Mathematics Subject Classification: 60G07