# The Exponentiated Gumbel Lomax Distribution: Properties and Applications

## DOI:

https://doi.org/10.6092/issn.1973-2201/10998## Keywords:

Exponentiated Gumbel distribution, Lomax distribution, Moments, Maximum likelihood estimation## Abstract

A new five-parameter distribution called exponentiated Gumbel Lomax (EGuL) is proposed and studied. The proposed distribution has reverse J-shaped, inverted bathtub-shaped and J-shaped hazard rate function making it suitable for modeling survival and lifetime data. The density of the new distribution is expressed as a linear combination of the exponentiated density of the Lomax distribution. We derive the explicit expression for the quantile function, moments, incomplete moment, moment of residual life, entropy and order statistics of EGuL distribution. The estimation of the parameters of the new model is done using the method of maximum likelihood. A simulation study is employed to ascertain the performance of the maximum likelihood estimates. Two applications are used to illustrate that the new distribution provides a better fit compared to other distributions with the same baseline.

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*Statistica*,

*82*(4), 433–459. https://doi.org/10.6092/issn.1973-2201/10998

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