Generalized Gompertz-power series distributions

摘要

In this paper, we introduce the generalized Gompertz-power series class ofdistributions which is obtained by compounding generalized Gompertz and powerseries distributions. This compounding procedure follows same way that waspreviously carried out by Silva et al. (2013) and Barreto-Souza et al. (2011)in introducing the compound class of extended Weibull-power series distributionand the Weibull-geometric distribution, respectively. This distributioncontains several lifetime models such as generalized Gompertz, generalizedGompertz-geometric, generalized Gompertz-poisson, generalized Gompertz-binomialdistribution, and generalized Gompertz-logarithmic distribution as specialcases. The hazard rate function of the new class of distributions can beincreasing, decreasing and bathtub-shaped. We obtain several properties of thisdistribution such as its probability density function, Shannon entropy, itsmean residual life and failure rate functions, quantiles and moments. Themaximum likelihood estimation procedure via a EM-algorithm is presented, andsub-models of the distribution are studied in details.