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.

Properties and estimation of a bivariate geometric model with locally constant failure rates / A. Barbiero. - In: ANNALS OF OPERATIONS RESEARCH. - ISSN 0254-5330. - (2019 Feb 12), pp. 1-20. [Epub ahead of print] [10.1007/s10479-019-03165-7]

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

Barbiero, Alessandro
2019-02-12

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.
Attainable correlations; Correlated counts; Failure rate; Gumbel–Barnett copula; Mean residual life; Method of moments; Stress–strength model; Decision Sciences (all); Management Science and Operations Research
Settore SECS-S/01 - Statistica
ANNALS OF OPERATIONS RESEARCH
http://www.kluweronline.com/issn/0254-5330
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/629655
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