|
Abstract
|
In this article, we introduce the Gompertz power series (GPS) class of
distributions which is obtained by compounding Gompertz and power
series distributions. This distribution contains several lifetime models
such as Gompertz-geometric (GG), Gompertz-Poisson (GP), Gompertzbinomial
(GB), and Gompertz-logarithmic (GL) distributions as special
cases. Sub-models of theGPS distribution are studied in details. The hazard
rate function of the GPS distribution can be increasing, decreasing,
and bathtub-shaped. We obtain several properties of the GPS distribution
such as its probability density function, and failure rate function,
Shannon entropy, mean residual life function, quantiles, and moments.
The maximum likelihood estimation procedure via a EM-algorithm is
presented, and simulation studies are performed for evaluation of this
estimation for complete data, and the MLE of parameters for censored
data. At the end, a real example is given.
|