Mean parameter modeling for an automobile insurance portfolio using Generalized Additive Models for Location, Scale and Shape (GAMLSS)

Abstract

In this study, Generalized Additive Models for location, scale and shape was deployed to model a typical automobile insurance portfolio. The data set used for this study comprises of seven variables, which are: Kilometres, Zone, Bonus, Make, Insured, Claims and Payments, it was compiled by a Swedish Committee on the Analysis of Risk Premium in Motor Insurance. The mean was modeled in terms of the explanatory variables although the GAMLSS has the capacity to model up to four parameters unlike the Generalized Lineal Models (GLMs) and Generalized Additive Models (GAMs). This allows for greater flexibility in modeling. In checking for over-dispersion, the negative binomial was used such that terms were dropped or added. Analysis revealed that all term were important and as such no terms could be dropped. When terms were added, analysis further showed that all the two way interaction terms are needed in the model except for the interaction between Kilometers and Zone. Results from the optimal model check gives the best model as those with separate smoothing terms for both Bonus and Kilometers.