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Closed-form maximum likelihood estimator for generalized linear models in the case of categorical explanatory variables: application to insurance loss modeling. (English) Zbl 1482.62005

Summary: Generalized linear models with categorical explanatory variables are considered and parameters of the model are estimated by an 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 an actuarial dataset to model insurance losses.

MSC:

62-08 Computational methods for problems pertaining to statistics
62P05 Applications of statistics to actuarial sciences and financial mathematics
62J12 Generalized linear models (logistic models)
91G05 Actuarial mathematics

Software:

DLMF; GAMLSS; MASS (R); R
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References:

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