Abstract
In this paper, we introduce a new class of distributions by compounding the generalized class of Lindley distributions with the power series family of distributions. This new class of distributions contains several lifetime subclasses, such as the Lindley power series, two-parameter Lindley power series and power Lindley power series distributions. It can also generate a number of statistical distributions, such as the power Lindley-Poisson, power Lindley geometric, power Lindley logarithmic and power Lindley binomial distributions. The proposed class is flexible in the sense that it can generate many new lifetime distributions as well as some existing distributions. Several properties of the proposed class are derived, such as hazard functions, limiting behavior, quantile functions, moments, moment-generating functions, and distributions of order statistics. Maximum likelihood estimation is used to estimate the model parameters of this new class. A simulation for a selective model is presented, and we demonstrate applications using three real datasets to show the flexibility and potential of the new class of distributions.