The McDonald Gompertz Distribution: Properties and Applications

This paper introduces a ve-parameter lifetime model called the McDonald Gompertz (McG) distribution, to extend the Gompertz, generalized Gompertz, generalized exponen- tial, beta Gompertz and Kumaraswamy Gompertz distributions, among several other mod- els. The hazard function of new distribution can be increasing, decreasing, upside-down bathtub and bathtub shaped. We obtain several properties of the McG distribution includ- ing moments, entropies, quantile and generating functions. We provide the density function of the order statistics and their moments. The parameter estimation is based on the usual maximum likelihood approach. We also provide the observed information matrix and dis- cuss inferences issues. The exibility and usefulness of the new distribution is illustrated by means of application to two real data sets.

Gompertz distribution; McDonald distribution; Maximum likelihood estimation;