Within non-life insurance, when actuaries are interested in estimating the frequency of
claims, the Poisson model is often considered. Although the literature sustains that it offers a
favourable statistical support for count data, the Poisson model implies the equidispersion
assumption that is a drawback in practical use when data is overdispersed. The literature
presents several reasons why data can be overdispersed and also many models to address the
variety of overdispersion found in data. In general, if the cause of overdispersion in Poisson
model is not diagnosed, the negative binomial models are commonly recommended. There
are a wide number of negative binomial models used, but for insurance data the more
intuitive ones are considered the NB1 and NB2 forms of the negative binomial distribution.