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.

中文翻译：

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类别解释变量下广义线性模型的封闭形式最大似然估计：在保险损失建模中的应用

考虑具有分类解释变量的广义线性模型，并通过精确的最大似然法估计模型的参数。讨论了最大似然估计序列的存在，并提出了对可能的链接函数的考虑。然后将重点放在两个特定的正分布上：帕累托1分布和平移对数正态分布。最后，该方法在精算数据集上进行了说明，以对保险损失进行建模。