The Generalized Weighted Lindley Distribution: Properties, Estimation and Applications

In this paper, we proposed a new lifetime distribution namely generalized weighted Lindley (GLW) distribution. The GLW distribution is a useful generalization of the weighted Lindley distribution, which accommodates increasing, decreasing, decreasing-increasing-decreasing, bathtub, or unimodal hazard functions, making the GWL distribution a flexible model for reliability data. A significant account of mathematical properties of the new distribution are presented. Different estimation procedures are also given such as, maximum likelihood estimators, method of moments, ordinary and weighted least-squares, percentile, maximum product of spacings and minimum distance estimators. The different estimators are compared by an extensive numerical simulations. Finally, we analyze two data sets for illustrative purposes, proving that the GWL outperform several usual three parameters lifetime distributions.