The extended Weibull distribution with its properties, estimation and modeling skewed data

Abstract

The present article introduces a new distribution called the odd log–logistic Lindley-Weibull (OLLLW) distribution that provides greater flexibility in modeling data in applied areas such as medicine and engineering. The OLLLW model provides left-skewed, symmetric, right-skewed, and reversed-J shaped densities. Its hazard function can be bathtub, unimodal, increasing or decreasing. The OLLLW density was expressed as a linear mixture of Weibull densities. Some distributional properties of the introduced model are derived. Its parameters are estimated using five classical estimators called, the maximum likelihood, Anderson–Darling, least-squares, Cramér-von Mises, and weighted least squares estimators. The performance of the proposed estimators is explored by detailed simulation results. The flexibility of the OLLLW distribution is studied by two real data sets from medicine and engineering sciences, showing that its capability to fit the data effectively than the Weibull, Fréchet Weibull, transmuted Weibull, gamma Weibull, transmuted exponentiated Weibull, and modified Weibull distributions.