A new flexible Weibull extension model: Different estimation methods and modeling an extreme value data

Huda M Alshanbari; Omalsad Hamood Odhah; Hazem Al-Mofleh; Zubair Ahmad; Saima K Khosa; Abd Al-Aziz Hosni El-Bagoury

doi:10.1016/j.heliyon.2023.e21704

A new flexible Weibull extension model: Different estimation methods and modeling an extreme value data

Heliyon. 2023 Oct 31;9(11):e21704. doi: 10.1016/j.heliyon.2023.e21704. eCollection 2023 Nov.

Authors

Huda M Alshanbari¹, Omalsad Hamood Odhah¹, Hazem Al-Mofleh^{2

3}, Zubair Ahmad⁴, Saima K Khosa⁵, Abd Al-Aziz Hosni El-Bagoury⁶

Affiliations

¹ Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia.
² Division of Science and Mathematics, Eureka College, Eureka, IL 61530, USA.
³ Department of Mathematics, Tafila Technical University, Tafila 66110, Jordan.
⁴ Department of Statistics, Quaid-i-Azam University, Islamabad 44000, Pakistan.
⁵ Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, SK, Canada.
⁶ Basic Sciences Department, Higher Institute of Engineering and Technology, EL-Mahala EL-Kobra, Egypt.

Abstract

The word extreme events refer to unnatural or undesirable events. Due to the general destructive effects on society and scientific problems in various applied fields, the study of extreme events is an important subject for researchers. Many real-life phenomena exhibit clusters of extreme observations that cannot be adequately predicted and modeled by the traditional distributions. Therefore, we need new flexible probability distributions that are useful in modeling extreme-value data in various fields such as the financial sector, telecommunications, hydrology, engineering, and meteorology. In this piece of research work, a new flexible probability distribution is introduced, which is attained by joining together the flexible Weibull distribution with the weighted T-X strategy. The new model is named a new flexible Weibull extension distribution. The distributional properties of the new model are derived. Furthermore, some frequently implemented estimation approaches are considered to obtain the estimators of the new flexible Weibull extension model. Finally, we demonstrate the utility of the new flexible Weibull extension distribution by analyzing an extreme value data set.

Keywords: Distributional properties; Estimation; Extreme value theory; Flexible Weibull extension distribution; Flood data.