On A Generalization Of Ling’S Binomial Distribution

Abstract

: In a sequence of n binary trials, distribution of the random variable Mn,k, denoting the number of overlapping success runs of length exactly k, is called Ling’s binomial distribution or Type II binomial distribution of order k. In this paper, we generalize Ling’s binomial distribution to Ling’s q-binomial distribution using Bernoulli trials with a geometrically varying success probability. An expression for the probability mass function of this distribution is derived. For q = 1, this distribution reduces to Ling’s binomial distribution.