Generalized exponential–power series distributions

In this paper, we introduce the generalized exponential–power series (GEPS) class of distributions, which is obtained by compounding generalized exponential and power series distributions. The compounding procedure follows the same way as previously carried out in introducing the complementary exponential–geometric (CEG) and the two-parameter Poisson–exponential (PE) lifetime distributions. This new class of distributions contains several lifetime models such as: CEG, PE, generalized exponential–binomial (GEB), generalized exponential–Poisson (GEP), generalized exponential–geometric (GEG) and generalized exponential–logarithmic (GEL) distributions as special cases.The hazard function of the GEPS distributions can be increasing, decreasing or bathtub shaped among others. We obtain several properties of the GEPS distributions such as moments, maximum likelihood estimation procedure via an EM-algorithm and inference for a large sample. Special distributions are studied in some detail. At the end, in order to show the flexibility and potentiality of the new class of distributions, we demonstrate applications of two real data sets.