Modeling Correlated Counts in Reliability Engineering

In this chapter, we review the problem of modeling correlated count data. Among the several methods that can be used for this scope, we focus on the copula approach, illustrating its advantages, but also possible limitations and issues arising in the discrete context if compared to the continuous case. After introducing the basic notions about copulas, the construction of a multivariate joint distribution is discussed and pseudorandom simulation and point estimation of copula-based models for count data are then outlined. Results related to minimum and maximum correlation between two assigned discrete marginal distributions are also described and put in connection with the choice of the copula to be used for modeling correlated counts. A numerical example and an application to a real dataset are provided.