**7. Conclusions**

In this article, a new flexible extension of an extreme distribution with three-parameter has been proposed, which generalized the inverse exponential distribution. The HRF of the new extension can be constant, increasing, increasing–constant, or unimodal shaped. Furthermore, it can be utilized for modelling asymmetric "positive and negative" as well as symmetric datasets and can be used to model over- and under-dispersed data. Thus, the new extension can be used effectively to model different kinds of data in several fields. The model parameters have been estimated utilizing the MLE approach. A simulation has been performed for different samples sizes, and it was found that the MLE technique works quite well for estimating the parameters for datasets considered herein. Finally, four data applications which illustrate the flexibility of the new extension and its excellence over other models have been also analyzed.

**Author Contributions:** Conceptualization, M.S.E. and M.E.-M.; methodology, M.S.E. and M.E.-M.; software, M.S.E. and M.E.-M.; validation, F.S.A. and K.M.A.; formal analysis, M.S.E., M.E.-M. and F.S.A.; resources, F.S.A. and K.M.A.; data curation, M.S.E. and M.E.-M.; writing—original draft preparation, M.S.E. and M.E.-M.; writing—review and editing, M.S.E. and M.E.-M.; visualization, F.S.A. and K.M.A.; project administration, M.S.E. and M.E.-M.; funding acquisition, F.S.A. and K.M.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** The data was mentioned along the paper.

**Acknowledgments:** This Research was supported by Taif University Researchers Supporting Project Number (TURSP-2020/217), Taif University, Taif, Saudi Arabia.

**Conflicts of Interest:** The authors declare no conflict of interest.
