Gompertz-Lindley distribution and associated inference

In this paper, we present a Gompertz-Lindley distribution obtained by mixing the frailty parameter of Gompertz distribution by Lindley distribution. The resulting model is more flexible having increasing, decreasing and upside-down bathtub shaped failure rate function. The parameters are estimated by the maximum likelihood method and their performance is examined by extensive simulation studies. Two practical examples are provided to illustrate the applicability of the model.