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An alternative derivation of some commons distributions functions: A post-model selection approach

Georges Nguefack-Tsague


This paper considers the view that a parametric distribution is a special case of family (finite or infinite) of models. As such, the estimation method (e.g., maximum likelihood estimation) can be viewed as model selection procedure (within model selection). In this case inference on the estimator of the parameter now falls under the theory of post-modelselection estimators (PMSEs), that is, estimators obtained after model selection. The point of view presented here, of regarding parameter estimation as model selection, leads to an alternative derivation of certain commons distributions, such as, Student, Fisher, Poisson, negative-binomial, beta-binomial, and noncentral chi-squared distributions. While the problem is restricted here to distributions functions this approach is applicable as well for nuisance parameter elimination.


point estimation, model selection, model averaging, distribution theory, probability

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