A new Markov Binomial distribution

Abstract

In this paper, we introduce a two state homogeneous Markov chain and define a geometric distribution related to this Markov chain. We define also the negative binomial distribution similar to the classical case and call it NB related to interrupted Markov chain. The new binomial distribution is related to the interrupted Markov chain. Some characterization properties of the Geometric distributions are given. Recursion formulas and probability mass functions for the NB distribution and the new binomial distribution are derived.Homogeneous Markov chain; Interrupted Markov chain; Geometric distribution related to Markov chain; In ated negative binomial distribution; New binomial distribution