In this paper, we introduce a new extension of the power Lindley distribution, called the odd
log-logistic Marshall-Olkin power Lindley distribution. We discuss some of its properties such
as the shapes of the density, hazard rate functions, quantile function, mixture representation,
moments, and order statistics. We also obtain the estimators of the parameters through
maximum likelihood approach. A simulation study is performed to evaluate the performance
of the maximum likelihood estimators. Finally, two real data sets are applied to illustrating of …

In this article, we introduce a new four-parameter odd log-logistic Marshall-Olkin power
Lindley distribution and discuss some of its properties. These include the shapes of the
density, hazard rate and quantile functions, mixture representation, moments, and order
statistics. Maximum likelihood estimation of the parameters and their estimated asymptotic
standard errors are derived. Three algorithms are proposed for generating random data from
the proposed distribution. A simulation study is carried out to examine the bias and mean …