A weighted Gompertz-G family of distributions for reliability and lifetime data analysis

Abstract

This article is set to push new boundaries with leading-edge innovations in statistical distribution for generating up-to-the-minute contemporary distributions by a mixture of the second record value of the Gompertz distribution and the classical Gompertz model (weighted Gompertz model) using T-X characterization, especially used for two-sided schemes that provide an accurate model. The quantile, ordinary, and complete moments, order statistics, probability, and moments generating functions, entropies, probability weighted moments, Lin’s condition random variable, reliability in multicomponent stress strength system, reversed, and moments of residuals life and other reliability characteristics in engineering, actuarial, economics, and environmental technology were derived in their closed form. To investigate and test the flexibility, viability, tractability, and performance of the proposed Weighted Gompertz-G (WGG) generated model, the shapes of some sub-models of the WGG model were examined. The shapes of the sub-models indicated J-shapes, increasing, decreasing, and bathtub hazard rate functions. The maximum likelihood estimation of the WGG-generated model parameters was examined. An illustration with simulation and real-life data analysis indicated that the WGG-generated model provides consistently better goodness-of-fit statistics than some competitive models in the literature.