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Properties and estimation of a bivariate geometric model with locally constant failure rates

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  • Alessandro Barbiero

    (Università degli Studi di Milano)

Abstract

Stochastic models for correlated count data have been attracting a lot of interest in the recent years, due to their many possible applications: for example, in quality control, marketing, insurance, health sciences, and so on. In this paper, we revise a bivariate geometric model, introduced by Roy (J Multivar Anal 46:362–373, 1993), which is very appealing, since it generalizes the univariate concept of constant failure rate—which characterizes the geometric distribution within the class of all discrete random variables—in two dimensions, by introducing the concept of “locally constant” bivariate failure rates. We mainly focus on four aspects of this model that have not been investigated so far: (1) pseudo-random simulation, (2) attainable Pearson’s correlations, (3) stress–strength reliability parameter, and (4) parameter estimation. A Monte Carlo simulation study is carried out in order to assess the performance of the different estimators proposed and application to real data, along with a comparison with alternative bivariate discrete models, is provided as well.

Suggested Citation

  • Alessandro Barbiero, 2022. "Properties and estimation of a bivariate geometric model with locally constant failure rates," Annals of Operations Research, Springer, vol. 312(1), pages 3-22, May.
    • Handle: RePEc:spr:annopr:v:312:y:2022:i:1:d:10.1007_s10479-019-03165-7
    DOI: 10.1007/s10479-019-03165-7
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    References listed on IDEAS

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    1. Lance Fiondella & Panlop Zeephongsekul, 2016. "Trivariate Bernoulli distribution with application to software fault tolerance," Annals of Operations Research, Springer, vol. 244(1), pages 241-255, September.
    2. C. R. Mitchell & A. S. Paulson, 1981. "A new bivariate negative binomial distribution," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(3), pages 359-374, September.
    3. Roy, D., 1993. "Reliability Measures in the Discrete Bivariate Set-Up and Related Characterization Results for a Bivariate Geometric Distribution," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 362-373, August.
    4. Sun, Kai & Basu, Asit P., 1995. "A characterization of a bivariate geometric distribution," Statistics & Probability Letters, Elsevier, vol. 23(4), pages 307-311, June.
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    Cited by:

    1. Shaomin Wu & Hongyan Dui & Linmin Hu, 2024. "Construction of copulas for bivariate failure rates," Annals of Operations Research, Springer, vol. 341(2), pages 1177-1189, October.

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