The Exponentiated Generalized Marshall–Olkin Family of Distribution: Its Properties and Applications

A new generator of continuous distributions called Exponentiated Generalized Marshall–Olkin-G family with three additional parameters is proposed. This family of distribution contains several known distributions as sub models. The probability density function and cumulative distribution function are expressed as infinite mixture of the Marshall–Olkin distribution. Important properties like quantile function, order statistics, moment generating function, probability weighted moments, entropy and shapes are investigated. The maximum likelihood method to estimate model parameters is presented. A simulation result to assess the performance of the maximum likelihood estimation is briefly discussed. A distribution from this family is compared with two sub models and some recently introduced lifetime models by considering three real life data fitting applications.