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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01781504
Contributor : Christophe Dutang <>
Submitted on : Sunday, August 25, 2019 - 1:59:00 PM
Last modification on : Thursday, April 1, 2021 - 2:18:02 PM
Long-term archiving on: : Friday, January 10, 2020 - 3:44:36 PM

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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. Computational Statistics, Springer Verlag, In press, ⟨10.1007/s00180-019-00918-7⟩. ⟨hal-01781504v3⟩

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