Abstract
In this paper, a new flexible generator of distributions is proposed. Some of its fundamental properties including quantile, skewness, kurtosis, hazard rate function, moments, mean deviations, mean time to failure, mean time between failure, availability and reliability function of consecutive linear and circular systems are studied. The hazard rate function can be increasing, decreasing, unimodal-bathtub, unimodal, bathtub, J and inverse J-shaped depending on its parameters values. After introducing the general class, two special models of the new family are discussed in detail. Maximum likelihood and Bayesian methods are used to estimate the model parameters. A detailed simulation study is carried out to examine the bias and mean square error of maximum likelihood and Bayesian estimators. We also illustrate the importance of the new family by means of two distinctive real data sets. It can serve as an alternative model to other lifetime distributions in the existing statistical literature for modeling positive and negative real data in many areas.