Morad Alizadeh

A four-parameter extended of Lindley distribution with application to lifetime data is introduced. It is calledextended Marshal-Olkin generalized Lindley distribution. Some mathematical properties such as moments, skewness,kurtosis and extreme value are derived. These properties with plots of density and hazard functions are shown the highflexibility of the mentioned distribution. The maximum likelihood estimations of proposed distribution parameters withasymptotic properties of these estimations are examined. A simulation study to investigate the performance of maximumlikelihood estimations is presented. Moreover, the performance and flexibility of the new distribution are investigated bycomparing with several generalizations of Lindley distribution through two real data sets. Finally, Bayesian analysis andefficiency of Gibbs sampling are provided based on the two real data sets