Discrete distributions related to success runs of lengthk in aulti-state markov chain
Nikolai Kolev, Leda D. Minkova · Communication in Statistics- Theory and Methods · 1997
We consider the time-homogeneous multi-state Markov chain {X , n ≥0} with states labeled as “0” (success) and “f” (failure), f = 1,2,… Let k be a fixed positive integer and SK be the event of a success run of length k in the sequence X0: X ,… In this article, joint probability generating functions for various statistics, related to the event SK0 are derived. In particular cases the exact distribution of the total number of successes S, the total number of failures F and the total number of trials N are deduced. The distribution of N is called the geometric distribution of order k for time-homogeneous {0,1,2,…}-valued Markov chain.