A probabilistic model for grouped events analysis

In this paper, the chains of rare events model and its applications are analyzed. This model was originally introduced in order to analyze events which can be produced as simple, double, triple, etc. Every one is distributed according to a Poisson law. A simple relation between the Poisson parameters was introduced in order to represent a contagion phenomenon. This model is particularly good to analyze grouped events like accidents, telephone calls, death, birth, failures production, reliability, etc. The best known model used in order to analyze grouped events is the compound Poisson. In this paper, we show a generalization of the chains of rare events model and show applications to reliability and queuing data. The results we obtain are compared with those obtained by other models