Weibull Lindley Distribution

Abstract

A new distribution is introduced based on compounding Lindley and Weibull distributions. This distribution contains Lindley and Weibull distributions as special cases. Several properties of the distribution are derived including the hazard rate function, moments, moment generating function, and Lorenz curve. An estimation procedure by the method of maximum likelihood and a simulation study to assess its performance are given. Three real data applications are presented to show that the new distribution fits better than known generalizations of the Lindley distribution.