An Extended Lindley Distribution with Application to Lifetime Data with Bayesian Estimation

A four-parameter extended of Lindley distribution with application to lifetime data is introduced.It is called extended Marshal-Olkin generalized Lindley distribution. Some mathematical propertiessuch as moments, skewness, kurtosis and extreme value are derived. These properties with plotsof density and hazard functions are shown the high flexibility of the mentioned distribution. Themaximum likelihood estimations of proposed distribution parameters with asymptotic properties ofthese estimations are examined. A simulation study to investigate the performance of maximumlikelihood estimations is presented. Moreover, the performance and flexibility of the new distributionare investigated by comparing with several generalizations of Lindley distribution through two realdata sets. Finally, Bayesian analysis and efficiency of Gibbs sampling are provided based on the tworeal data sets.