Abstract: This article presents a new generalization of the Poisson distribution, with the parameters ? > 0 and ? > 0, using the Marshall and Olkin (1997) scheme and adding a parameter to the classical Poisson distribution. The particular case of ? = 1 gives the Poisson distribution. The new distribution is unimodal and has a failure rate that monotonically increases or decreases depending on the value of the parameter ?. After reviewing some of the properties of this distribution, we investigated the question of parameter estimation. Expected frequencies were calculated for two data sets, one with an index of dispersion larger than one and the other with an index of dispersion smaller than one. In both cases the distribution provided a very satisfactory fit.

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