Properties and estimation of a bivariate geometric model with locally constant failure rates
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.
KeywordsAttainable correlations Correlated counts Failure rate Gumbel–Barnett copula Method of moments Mean residual life Stress–strength model
I would like to thank the Editor-in-Chief, the Guest Editor, and the anonymous referees for their valuable comments on an earlier draft of this article. I acknowledge the financial support to the present research by the University of Milan (Piano di Sostegno alla Ricerca 2015/2017-Linea 2A).
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