Abstract
Abstract In this article, we propose a Gompertz-two-parameter-Lindley distribution by mixing the frailty parameter of the Gompertz distribution with a two-parameter Lindley distribution. The structural properties of the model, such as shape properties, cumulative distribution, quantile functions, moment, moment generating function, failure rate function, mean residual function, and stochastic orders, were derived. Moreover, the unknown parameters are estimated by the profile log likelihood algorithm, and their performance is examined by simulation studies. Finally, a real data example is used to demonstrate the application of the proposed model.
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