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Abstract
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In this paper, we introduce a new three-parameter generalized version of the Gompertz model called the odd log-logistic Gompertz (OLLGo) distribution. It includes some
well-known lifetime distributions such as Gompertz (Go) and odd log-logistic exponential
(OLLE) as special sub-models. This new distribution is quite flexible and can be used
effectively in modeling survival data and reliability problems. It can have a decreasing,
increasing and bathtub-shaped failure rate function depending on its parameters. Some
mathematical properties of the new distribution, such as closed-form expressions for the
density, cumulative distribution, hazard rate function, the kth order moment, moment
generating function and the quantile measure are provided. We discuss maximum likeli-
hood estimation of the OLLGo parameters as well as three other estimation methods from
one observed sample. The flexibility and usefulness of the new distribution is illustrated by means of application to a real data set.
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