Abstract: In this paper, a new discrete two-parameter distribution ? ? ? ? {0} and 0 < ? < 1, the Geometric ArcTan (GAT) distribution is introduced. The geometric distribution is a limiting case of this model when ? tends to zero. Similarly to the the latter distribution, this probabilistic family is unimodal but the mode can be located at zero or in other point of the support. Then, after deriving some of its more relevant properties , the issue of parameter investigation is investigated. Next, the GAT distribution is used to explain the demand for health services by means of a regression model. Numerical results show that this new model outperforms the negative binomial distribution

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