A Class of Lindley and Weibull Distributions

Abstract

In this paper, we introduce a class of Lindley and Weibull distributions (LW) that are useful for modeling lifetime data with a comprehensive mathematical treatment. The new class of generated distributions includes some well-known distributions, such as exponential, gamma, Weibull, Lindley, inverse gamma, inverse Weibull, inverse Lindley, and others. We provide closed-form expressions for the density, cumulative distribution, survival function, hazard rate function, moments, moments generating function, quantile, and stochastic orderings. Moreover, we discuss maximum likelihood estimation and the algorithm for computing the parameters estimates. Some sub models are discussed as an illustration with real data sets to show the flexibility of this class.