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Abstract
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In this article, we introduce a new three-parameter odd log-logistic logarithmic Lindley distribution
and discuss some of its properties. These include the shapes of the density and hazard rate functions,
mixture representation, the moments, the quantile function, and order statistics. Maximum likelihood
estimation of the parameters and their estimated asymptotic standard errors are derived. Three algo-
rithms are proposed for generating random data from the proposed distribution. A simulation study
is carried out to examine the bias and mean square error of the maximum likelihood estimators of the
parameters. An application of the model to two real data sets is presented finally and compared with the
fit attained by some other well-known two and three-parameter distributions for illustrative purposes.
It is observed that the proposed model has some advantages in analyzing lifetime data as compared to
other popular models in the sense that it exhibits varying shapes and shows more flexibility than many
currently available distributions.
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