@inproceedings{46d20e19ec394291b8d5b7a135babbf2,
title = "A New Compound Negative Binomial Distribution and Its Applications in Reliability",
abstract = "A new negative binomial distribution (NBS) is proposed by introducing the concept of sparse connection. Finite Markov chain imbedding approach is used to obtain NBS for the cases of independent trials, first-order Markov dependent trials and high-order Markov dependent trials respectively. New compound negative binomial distributions called CNBS and CMNBS for independent and Markov cases respectively are derived by means of phase-type representations. The new compound negative binomial distributions can be applied in the shock models and start-up demonstration tests in the field of reliability. Numerical examples based on shock models are then presented to demonstrate the applicability of the new distribution.",
keywords = "Compound random variable, Finite Markov chain imbedding approach, Phase-type distribution, Sparse connection",
author = "Xiaoyue Wang and Xian Zhao and Jinglei Sun",
note = "Publisher Copyright: {\textcopyright} 2020 IEEE.; 2020 Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modeling, APARM 2020 ; Conference date: 20-08-2020 Through 23-08-2020",
year = "2020",
month = aug,
doi = "10.1109/APARM49247.2020.9209481",
language = "English",
series = "2020 Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modeling, APARM 2020",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
booktitle = "2020 Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modeling, APARM 2020",
address = "United States",
}