In the literature, two-parameter distributions which exhibit all three types of decreasing, increasing and bathtub shape hazard rate functions are very few.
In this paper, we propose a new two-parameter distribution, called Gompertz-weighted exponential distribution, having these three types of hazard rate functions. The proposed distribution is obtained by mixing the frailty parameter of the Gompertz distribution by weighted exponential distribution.
The parameters are estimated by the maximum likelihood method and their performance is examined by extensive
simulation studies. Three real data applications are provided to illustrate the superiority of the proposed distribution
over many well known two-parameter distributions.
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