A new generalization of the Gompertz Makeham distribution: theory and application in reliability

In this paper, a new five-parameter distribution called Marshall-Olkin Gompertz Makeham Distribution (MOGM) is proposed. This new model can be applied to the analysis of lifetime data, engineering, and actuaries. In addition, several properties of the proposed model such as mode, moment, Reyni entropy, Tsallis entropy, quantile function, and decreasing and unimodal hazard rate function were also investigated. The unknown parameters of MOGM distribution were estimated using Maximum Likelihood Estimation (MLE) and Bayes methods. Then, these methods were compared using Monte Carlo simulation and the best estimator was introduced accordingly. Finally, some other applications of the proposed model were illustrated to show its usefulness and efficiency.