Generalized Gompertz-power series distributions

Year 2016, Volume: 45 Issue: 5, 1579 - 1604, 01.10.2016

Saeed Tahmasebi Ali Akbar Jafari

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

• [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.
• [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.