A new Gompertz-three-parameter-lindley distribution for modeling survival time data

Abstract

In this paper, a new survival distribution is introduced. It is a mixture of the Gompertz distribution and three-parameter-Lindley distribution. The statistical properties of the proposed distribution including the shape properties, cumulative distribution, quantile functions, moment generating function, failure rate function, mean residual function, and stochastic orders are studied. Moreover, a new regression model based on the proposed distribution is presented. Maximum likelihood estimators (MLEs) of unknown parameters are obtained via differential evolution algorithms, and simulation studies are conducted to evaluate the consistency of the MLEs. Finally, the proposed model and its regression model are applied to a real dataset and compared with other well-known models, demonstrating their superior performance, particularly for heavy-tailed data.