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.