A new generalized Lindley-Weibull class of distributions: Theory, properties and applications

We propose a new generalized class of distributions called Lindley-Weibull Power Series (LWPS) distributions and their special case called Lindley-Weibull logarithmic (LWL) distributions. Structural properties of the LWPS class of distributions and its sub-model LWL distribution including moments, order statistics, Rényi entropy, mean and median deviations, Bonferroni and Lorenz curves, and maximum likelihood estimates are derived. A simulation study to examine the bias and mean square error of the maximum likelihood estimators for each parameter is presented. Finally, real data examples are presented to illustrate the applicability and usefulness of the proposed class of distributions.