Marshall olkin extended exponentiated Gamma distribution and its applications

Abstract

Different methods for obtaining new probability distributions have been introduced in the literature in recent years, for example, (Gupta et al., 1998) proposed an interesting uni-parametric lifetime distribution, Exponentiated Gamma (EG), which hazard function has increasing and bathtub shapes. In this paper, we build a new two-parameters distribution, the Marshall Olkin Extended Exponentiated Gamma (MOEEG) distribution, which is derived from the Marshall-Olkin method and the EG distribution. The hazard function of this new distribution can accommodate monotonic, non-monotonic and unimodal shapes, allowing a better fit to greater data variability. In addition to the great flexibility of fitting the data, it contains only two parameters providing a simple parameter estimation procedure, unlike other distributions proposed in the literature that have three or more parameters. Some properties of the new distribution considered in this paper are presented such as $n$ -th time, $r$ -th moment of residual life, $r$ -thmoment of residual life inverted, stochastic ordering, entropy, mean deviation, Bonferroni and Lorenz curve, skewness, kurtosis, order statistics, and stress-strength parameter. We also apply two different estimation methods, maximum likelihood and Bayesian approach. Real data applications are presented to illustrate the usefulness of this new distribution.