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Discrete analogues of continuous bivariate probability distributions

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  • Alessandro Barbiero

    (Università degli Studi di Milano)

Abstract

In many real-world applications, the phenomena of interest are continuous in nature and modeled through continuous probability distributions, but their observed values are actually discrete and hence it would be more reasonable and convenient to choose an appropriate (multivariate) discrete distribution generated from the underlying continuous model preserving one or more important features. In this paper, two methods are discussed for deriving a bivariate discrete probability distribution from a continuous one by retaining some specific features of the original stochastic model, namely (1) the joint density function, or (2) the joint survival function. Examples of applications are presented, which involve two types of bivariate exponential distributions, in order to illustrate how the discretization procedures work and show whether and to which extent they alter the dependence structure of the original model. We also prove that some bivariate discrete distributions that were recently proposed in the literature can be actually regarded as discrete counterparts of well-known continuous models. A numerical study is presented in order to illustrate how the procedures are practically implemented and to present inferential aspects. Two real datasets, considering correlated discrete recurrence times (the former) and counts (the latter) are eventually fitted using two discrete analogues of a bivariate exponential distribution.

Suggested Citation

  • Alessandro Barbiero, 2022. "Discrete analogues of continuous bivariate probability distributions," Annals of Operations Research, Springer, vol. 312(1), pages 23-43, May.
    • Handle: RePEc:spr:annopr:v:312:y:2022:i:1:d:10.1007_s10479-019-03388-8
    DOI: 10.1007/s10479-019-03388-8
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    References listed on IDEAS

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    1. Bebbington, Mark & Lai, Chin-Diew & Wellington, Morgan & Zitikis, RiÄ ardas, 2012. "The discrete additive Weibull distribution: A bathtub-shaped hazard for discontinuous failure data," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 37-44.
    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. Jean-Sébastien Tancrez & Philippe Chevalier & Pierre Semal, 2011. "Probability masses fitting in the analysis of manufacturing flow lines," Annals of Operations Research, Springer, vol. 182(1), pages 163-191, January.
    4. Tomasz Kozubowski & Seidu Inusah, 2006. "A Skew Laplace Distribution on Integers," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(3), pages 555-571, September.
    5. 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.
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