GCRIS :: Search

Search Results

Now showing 1 - 2 of 2

Citation - WoS: 2
Citation - Scopus: 2
Computing Waiting Time Probabilities Related To (k_{1< k_{2< ..., k_l< Pattern}}
(Springer, 2023) Chadjiconstantinidis, Stathis; Eryilmaz, Serkan
For a sequence of multi-state trials with l possible outcomes denoted by {1, 2, ..., l}, let E be the event that at least k(1) consecutive is followed by at least k(2) consecutive 2s,..., followed by at least k(l) consecutive ls. Denote by T-r the number of trials for the rth occurrence of the event E in a sequence of multi-state trials. This paper studies the distribution of the waiting time random variable T-r when the sequence consists of independent and identically distributed multi-state trials. In particular, distributional properties of T-r are examined via matrix-geometric distributions.
Citation - WoS: 14
Citation - Scopus: 17
Compound Geometric Distribution of Order k
(Springer, 2017) Koutras, Markos V.; Eryilmaz, Serkan
The distribution of the number of trials until the first k consecutive successes in a sequence of Bernoulli trials with success probability p is known as geometric distribution of order k. Let T (k) be a random variable that follows a geometric distribution of order k, and Y (1),Y (2),aEuro broken vertical bar a sequence of independent and identically distributed discrete random variables which are independent of T (k) . In the present article we develop some results on the distribution of the compound random variable Y-t.