Distributions of $$({k}_{1},{k}_{2},\dots,{k}_{m})$$ ( k 1, k 2, ⋯, k m ) -runs with Multi-state Trials

Xian Zhao, Yanbo Song, Xiaoyue Wang () and Zhiyue Lv
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Xian Zhao: Beijing Institute of Technology
Yanbo Song: Beijing Institute of Technology
Xiaoyue Wang: Beijing Technology and Business University
Zhiyue Lv: AVIC China Aero-Polytechnology Establishment

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 4, 2689-2702

Abstract: Abstract In this paper, six new $$({k}_{1},{k}_{2},\dots ,{k}_{m})$$ ( k 1 , k 2 , ⋯ , k m ) -runs with multi-state trials are proposed creatively, which can satisfy the practical needs in many fields. The exact distributions of proposed runs are obtained by applying finite Markov chain imbedding approach. This paper not only studies the case of independent identical distribution (i.i.d.) multi-state trials, but also independent non-identical distribution (non-i.i.d.) multi-state trials. Numerical examples have served the purpose to illustrate the effectiveness of the proposed approach. This study is of reference value and application significance for similar runs.

Keywords: $$({k}_{1}; {k}_{2}; \dots; {k}_{m})$$ ( k 1; k 2; ⋯; k m ) -runs; Multi-state trials; Exact distributions; Finite Markov chain imbedding approach (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-022-09948-z

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