  Based on the recent paper by Delong et al. (2021), two distributions for the
total claims amount (loss cost) are considered: Compound Poisson-gamma (CPG)
and Tweedie. Each is used as an underlying distribution in the Bonus-Malus
Scale (BMS) model described in the paper by Boucher (2023). The BMS model links
the premium of an insurance contract to a function of the insurance experience
of the related policy. In other words, the idea is to model the increase and
the decrease in premiums for insureds that do or do not file claims. Therefore,
our proposed models can be seen as a generalization of the paper of Delong et
al. (2021) and an extension of the work of Boucher (2023). We applied our
approach to a sample of data from a major insurance company in Canada. Data fit
and predictability were analyzed. We showed that the studied models are
exciting alternatives to consider from a practical point of view, and that
predictive ratemaking models can address some importantpractical
considerations.
