Distributions of (k1, k2, ⋯ , km) -runs with Multi-state Trials

Xian Zhao; Yanbo Song; Xiaoyue Wang; Zhiyue Lv

doi:10.1007/s11009-022-09948-z

Distributions of (k₁, k₂, ⋯ , k_m) -runs with Multi-state Trials

Xian Zhao
, Yanbo Song
, Xiaoyue Wang^*
, Zhiyue Lv

^*Corresponding author for this work

School of Economics

Beijing Institute of Technology
Beijing Technology and Business University
AVIC China Aero-poly Technology Establishment

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

In this paper, six new (k₁, k₂, ⋯ , 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.

Original language	English
Pages (from-to)	2689-2702
Number of pages	14
Journal	Methodology and Computing in Applied Probability
Volume	24
Issue number	4
DOIs	https://doi.org/10.1007/s11009-022-09948-z
Publication status	Published - Dec 2022

Keywords

(k, k, ⋯ , k) -runs
Exact distributions
Finite Markov chain imbedding approach
Multi-state trials

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10.1007/s11009-022-09948-z

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title = "Distributions of (k1, k2, ⋯ , km) -runs with Multi-state Trials",

abstract = "In this paper, six new (k1, k2, ⋯ , km) -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.",

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author = "Xian Zhao and Yanbo Song and Xiaoyue Wang and Zhiyue Lv",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

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AU - Zhao, Xian

AU - Song, Yanbo

AU - Wang, Xiaoyue

AU - Lv, Zhiyue

PY - 2022/12

Y1 - 2022/12

N2 - In this paper, six new (k1, k2, ⋯ , km) -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.

AB - In this paper, six new (k1, k2, ⋯ , km) -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.

KW - (k, k, ⋯ , k) -runs

KW - Exact distributions

KW - Finite Markov chain imbedding approach

KW - Multi-state trials

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SP - 2689

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JO - Methodology and Computing in Applied Probability

JF - Methodology and Computing in Applied Probability

IS - 4

ER -

Distributions of (k₁, k₂, ⋯ , k_m) -runs with Multi-state Trials

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Keywords

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