@Article{cmc.2020.010887,
AUTHOR = {Rashad Bantan, Amal S. Hassan, Mahmoud Elsehetry},
TITLE = {Generalized Marshall Olkin Inverse Lindley Distribution with  Applications},
JOURNAL = {Computers, Materials \& Continua},
VOLUME = {64},
YEAR = {2020},
NUMBER = {3},
PAGES = {1505--1526},
URL = {http://www.techscience.com/cmc/v64n3/39442},
ISSN = {1546-2226},
ABSTRACT = {In this article, a new generalization of the inverse Lindley distribution is 
introduced based on Marshall-Olkin family of distributions. We call the new distribution, 
the generalized Marshall-Olkin inverse Lindley distribution which offers more flexibility 
for modeling lifetime data. The new distribution includes the inverse Lindley and the 
Marshall-Olkin inverse Lindley as special distributions. Essential properties of the 
generalized Marshall-Olkin inverse Lindley distribution are discussed and investigated 
including, quantile function, ordinary moments, incomplete moments, moments of 
residual and stochastic ordering. Maximum likelihood method of estimation is considered 
under complete, Type-I censoring and Type-II censoring. Maximum likelihood estimators 
as well as approximate confidence intervals of the population parameters are discussed. 
A comprehensive simulation study is done to assess the performance of estimates based 
on their biases and mean square errors. The notability of the generalized Marshall-Olkin 
inverse Lindley model is clarified by means of two real data sets. The results showed the 
fact that the generalized Marshall-Olkin inverse Lindley model can produce better fits 
than power Lindley, extended Lindley, alpha power transmuted Lindley, alpha power 
extended exponential and Lindley distributions.},
DOI = {10.32604/cmc.2020.010887}
}