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Symmetry
Volume 13
Issue 5
10.3390/sym13050745
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Article

A Flexible Extension to an Extreme Distribution

by
Mohamed S. Eliwa
1,
Fahad Sameer Alshammari
2,
Khadijah M. Abualnaja
3 and
Mahmoud El-Morshedy
2,4,*
1
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
2
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
3
Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
4
Department of Statistics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
*
Author to whom correspondence should be addressed.
Symmetry 2021, 13(5), 745; https://doi.org/10.3390/sym13050745
Submission received: 16 March 2021 / Revised: 14 April 2021 / Accepted: 19 April 2021 / Published: 23 April 2021
(This article belongs to the Special Issue Symmetric Distributions, Moments and Applications)
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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 probability distributions; skewed and symmetric data; maximum likelihood estimation; hazard rate function; censored samples

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MDPI and ACS Style

Eliwa, M.S.; Alshammari, F.S.; Abualnaja, K.M.; El-Morshedy, M. A Flexible Extension to an Extreme Distribution. Symmetry 2021, 13, 745. https://doi.org/10.3390/sym13050745

AMA Style

Eliwa MS, Alshammari FS, Abualnaja KM, El-Morshedy M. A Flexible Extension to an Extreme Distribution. Symmetry. 2021; 13(5):745. https://doi.org/10.3390/sym13050745

Chicago/Turabian Style

Eliwa, Mohamed S., Fahad Sameer Alshammari, Khadijah M. Abualnaja, and Mahmoud El-Morshedy. 2021. "A Flexible Extension to an Extreme Distribution" Symmetry 13, no. 5: 745. https://doi.org/10.3390/sym13050745

APA Style

Eliwa, M. S., Alshammari, F. S., Abualnaja, K. M., & El-Morshedy, M. (2021). A Flexible Extension to an Extreme Distribution. Symmetry, 13(5), 745. https://doi.org/10.3390/sym13050745

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