A New Log Lindley Distribution with Applications

Abstract

This paper introduces a new generalization of the Lindley distribution introduced by Lindley (1958), using the basic idea of Pappas et al. (2012), and along the lines of Marshall and Olkin (1997). The new distribution is a compound of the Lindley and Logarithmic distributions. We refer to the new model as the Logarithmic-Lindley (Log-L) distribution. This model is capable of modeling various shapes of aging and failure criteria. The properties of the new model are discussed and the maximum likelihood, maximum product spacings and least square estimation methods are used to evaluate the parameters involved. Explicit expressions are derived for the moments and examine the order statistics. Finally, the usefulness of the new model for modeling reliability data is illustrated using a two real data sets with simulation study.