Poisson model
An excellent definition of the law of rare events is given in Cameron and Trivedi
(1998). The authors state that the total number of events will follow, approximately, the
Poisson distribution if an event may occur in any of a large of trials but the probability of
occurrence in any given trial is small. In the context of actuarial literature, comprehensive
references on Poisson distribution, used as the main tool in estimating the claim frequency,
are Dionne and Vanasse (1989), 1992), Denuit and Lang (2004), Gourieroux and Jasiak
(2004), Yip and Yau (2005) and many others.