Abstract

We introduce a four-parameter extension of the exponential distribution, which has the Exponentiated exponential, Marshall-Olkin exponential, and exponential distribution as sub-models. The proposed distribution has two important properties: it involves more parameters than the baseline model to obtain more flexibility and the extra parameters have a clear interpretation and representation. The proposed model is more flexible than any of its sub-models. Its probability density function can be monotone increasing, decreasing, or unimodal and its associated hazard rate may be increasing, decreasing, unimodal or bathtub-shaped. Statistical expression is obtained for certain structural statistical properties such as ordinary and incomplete moments, moment generating function, order statistics, quantile function, reliability function, and Renyi entropy. The maximum likelihood estimation method is used to obtain the estimates of the model parameters. An application of the new model to two lifetime data demonstrates the flexibility of the model.

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