Computing waiting time probabilities related to (k1, k2, ..., kl) pattern

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Date
2023-11-26
Authors
Chadjiconstantinidis, Stathis
Eryılmaz, Serkan
Journal Title
Journal ISSN
Volume Title
Publisher
Statistical Papers
Abstract
For a sequence of multi-state trials with l possible outcomes denoted by f1; 2; :::; lg, let E be the event that at least k1 consecutive 1s followed by at least k2 consecutive 2s,..., followed by at least kl consecutive ls. Denote by Tr 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 Tr when the sequence consists of independent and identically distributed multi-state trials. In particular, distributional properties of Tr are examined via matrix-geometric distributions.
Description
Statistical Papers (2023) 64: 1373-1390, https://doi.org/10.1007/s00362-022-01351-7, aUniversity of Piraeus, Greece, bAtilim University, Turkey
Keywords
Matrix-geometric distributions
Citation
https://doi.org/10.1007/s00362-022-01351-7