Parameters estimation for a new generalized geometric distribution

Abstract

A generalization of the geometric distribution is obtained after mixing the Poisson distribution with the generalized exponential distribution in Marshall and Olkin in 1997. The discrete distribution is defined through a new special function also introduced in this manuscript. Unimodality is highlighted among the properties of this two-parameter distribution. A favorable maximum likelihood parameter estimation scheme for the discrete distribution is introduced based on a quadrature method by approximating the special function by the trapezoidal rule. The effectiveness of the method is confirmed by expectation-maximization (EM) algorithm. An application to explain the demand for health services is given.