Another generalization of the geometric distribution

Abstract

A new generalization of the geometric distribution with parameters α>0 and 0<Θ<1 is obtained in this paper. This can be done either by using the Marshall and Olkin (Biometrika 84(3), 641-652, 1997) scheme and adding a parameter to the geometric distribution or by starting with the generalized exponential distribution in Marshall and Olkin (Biometrika 84(3), 641-652, 1997) and discretizing this continuous distribution. The particular case α=1 led us to the geometric distribution. After reviewing some of its properties, we investigated the question of parameter estimation. The new distribution is unimodal with a failure rate that is monotonically increasing or decreasing, depending on the value of the parameter α. Expected frequencies were calculated for two overdispersed and infradispersed examples, and the distribution was found to provide a very satisfactory fit.