Closed form Maximum Likelihood Estimator for Generalized Linear Models in the case of categorical explanatory variables: Application to insurance loss modelling

Alexandre Brouste (1) , Christophe Dutang (2) , Tom Rohmer (1)

1 LMM - Laboratoire Manceau de Mathématiques
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

Generalized Linear Models with categorical explanatory variables are considered and parameters of the model are estimated with an original exact maximum likelihood method. The existence of a sequence of maximum likelihood estimators is discussed and considerations on possible link functions are proposed. A focus is then given on two particular positive distributions: the Pareto 1 distribution and the shifted log-normal distributions. Finally, the approach is illustrated on a actuarial dataset to model insurance losses.

Mots clés: Generalized linear model; heavy-tailed distributions; insurance claim modeling

Domaines: Statistiques [math.ST]

Alexandre Brouste, Christophe Dutang, Tom Rohmer. Closed form Maximum Likelihood Estimator for Generalized Linear Models in the case of categorical explanatory variables: Application to insurance loss modelling. 2018. ⟨hal-01781504v1⟩