On an extension of the exponential-geometric distribution

Various statistical properties and reliability aspects of a two-parameter distribution with decreasing and increasing failure rate are explored; the model includes the exponential-geometric distribution [Marshall and Olkin, 1997. Biometrika 84, 641-652; Adamidis and Loukas, 1998. Statist. Probab. Lett. 39, 35-42] as a special case. Characterizations are given and the estimation of parameters is studied by the method of maximum likelihood. An EM algorithm [Dempster et al., 1977. J. R. Statist. Soc. B. 39, 1-38] is proposed for computing the estimates, and expressions for their asymptotic variances and covariances are derived. Numerical examples based on real data are included.