On the Topp-Leone Generalized Power Weibull Distribution: Properties, Applications and Regression

Abstract The Topp-Leone generalized power Weibull distribution, which is an extension of generalized power Weibull, is proposed and its properties explored. The failure rate of the proposed distribution exhibits increasing, reversed J, upside-down bathtub, and bathtub shapes. Some statistical properties are obtained: quantile function, moments, moment generating function, incomplete moment, mean and median deviations, mean residual life function, and Lorenz as well as Bonferroni curves. The maximum likelihood estimation approach is deployed to estimate the model parameters. Simulation studies are conducted to evaluate the performance and accuracy of the maximum likelihood estimates of the model parameters. Applications of the model to real datasets are presented. A location-scale regression model is also developed for the proposed model and its application has been demonstrated with a real dataset. Keywords: Bonferroni, Deviation, Mimicked, Simulation, and Upside-down Bathtub.