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

Abstract

In this paper, a new five-parameter distribution is proposed that is called MarshallOlkin Gompertz Makeham distribution(MOGM). This new model is applicable in analysis lifetime data, engineering and actuarial. In this research, some properties of the new model such as mode, moment, Reyni entropy, Tsallis entropy, quantile function and the hazard rate function which is decreasing and unimodal, are studied. The unknown parameters of the MOGM distribution are estimated using the maximum likelihood and Bayes methods. Then these methods are compared using Monte Carlo simulation and the best estimator is proposed. Finally, applications of the proposed model are illustrated to show its usefulness.

Keywords

• gompertz makeham distribution
• reliability
• failure time
• estimation parameters
• simulation
• model selection criteria.