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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.