*Article* **A Flexible Extension to an Extreme Distribution**

**Mohamed S. Eliwa 1, Fahad Sameer Alshammari 2, Khadijah M. Abualnaja 3 and Mahmoud El-Morshedy 2,4,\***



**Abstract:** The aim of this paper is not only to propose a new extreme distribution, but also to show that the new extreme model can be used as an alternative to well-known distributions in the literature to model various kinds of datasets in different fields. Several of its statistical properties are explored. It is found that the new extreme model can be utilized for modeling both asymmetric and symmetric datasets, which suffer from over- and under-dispersed phenomena. Moreover, the hazard rate function can be constant, increasing, increasing–constant, or unimodal shaped. The maximum likelihood method is used to estimate the model parameters based on complete and censored samples. Finally, a significant amount of simulations was conducted along with real data applications to illustrate the use of the new extreme distribution.

**Keywords:** probability distributions; skewed and symmetric data; maximum likelihood estimation; hazard rate function; censored samples
