Logarithmic inverse Lindley distribution: Model, properties and applications

In this paper, we proposed a new extension of inverse Lindley distribution called Logarithmic inverse Lindley (LIL). To this end, an extension of the Marshall-Olkin generalization approach, by Marshall and Olkin (1997), has been used. This generalization method was introduced by Pappas et al. (2012). It is shown that the distribution belongs to the family of upside-down bathtub shaped distribution. The properties of the LIL distribution are discussed and the maximum likelihood estimation is used to evaluate the parameters involved. The moments of the new model are derived. We use the Lambert function to derive explicit expressions for the quantiles and its special case (the median). A Monte Carlo simulation study is presented to exhibit the performance and accuracy of maximum likelihood estimates of the LIL model parameters. Finally, the usefulness of the new model for modeling reliability data is illustrated using a real data set to show the performance of the new distribution. (C) 2018 The Author. Production and hosting by Elsevier B.V. on behalf of King Saud University.