Generalized Gompertz-power series distributions

Abstract

In this paper, we introduce the generalized Gompertz-power series class of distributions which is obtained by compounding generalized Gompertz and power series distributions. This compounding procedure follows same way that was previously carried out by [25] and [3] in introducing the compound class of extended Weibull-power series distribution and the Weibull-geometric distribution, respectively. This distribution contains several lifetime models such as generalized Gompertz, generalized Gompertz-geometric, generalized Gompertz-poisson, generalized Gompertz-binomial distribution, and generalized Gompertzlogarithmic distribution as special cases. The hazard rate function of the new class of distributions can be increasing, decreasing and bathtub-shaped. We obtain several properties of this distribution such as its probability density function, Shannon entropy, its mean residual life and failure rate functions, quantiles and moments. The maximum likelihood estimation procedure via a EM-algorithm is presented, and sub-models of the distribution are studied in details. 

Keywords

• EM algorithm,Generalized Gompertz distribution,Maximum likelihood estimation,Power series distributions

References

1. [3] Barreto-Souza, W., Morais, A. L. and Cordeiro, G. M. The Weibull-geometric distribution, Journal of Statistical Computation and Simulation, 81 (5), 645-657, 2011.
2. [25] Silva, R. B., Bourguignon, M., Dias, C. R. B. and Cordeiro, G. M. The compound class of extended Weibull power series distributions, Computational Statistics and Data Analysis, 58, 352-367, 2013.