Abstract
For a sequence of multi-state trials with l possible outcomes denoted by \( \left\{ 1,2,\ldots ,l\right\} \), let E be the event that at least \(k_{1}\) consecutive 1s 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.
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Chadjiconstantinidis, S., Eryilmaz, S. Computing waiting time probabilities related to \( (k_{1},k_{2},\ldots ,k_{l})\) pattern. Stat Papers 64, 1373–1390 (2023). https://doi.org/10.1007/s00362-022-01351-7
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DOI: https://doi.org/10.1007/s00362-022-01351-7