| Sammanfattning: | In this dissertation we present a review of the generalized Poisson distribution. This distribution is an alternative to allow over dispersion in discrete models. The flexibility of the value of the variance in relation to the average is due to the presence of an additional parameter with respect to the Poisson distribution. The generalized Poisson distribution was first introduced as an element of the class of Lagrangian distributions. In this work it is proposed a new parametrization in terms of the Lambert W function that allows us to relate it to the class of power series distributions and, therefore, to use well known properties and characteristics of this class. In addition, we will present applications from different areas of knowledge, inference methods for both point and interval estimation and hypotheses testing. Were also review some R packages which deal with this distribution.
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