TY - JOUR
T1 - The Weighted Flexible Weibull Model
T2 - Properties, Applications, and Analysis for Extreme Events
AU - Ramaki, Ziaurrahman
AU - Alizadeh, Morad
AU - Tahmasebi, Saeid
AU - Afshari, Mahmoud
AU - Contreras-Reyes, Javier E.
AU - Yousof, Haitham M.
N1 - Publisher Copyright:
© 2025 by the authors.
PY - 2025/4
Y1 - 2025/4
N2 - The weighted flexible Weibull distribution focuses on its unique point of flaunting a bathtub-shaped hazard rate, characterized by an initial increase followed by a drop over time. This property plays a major role in reliability analysis. In this paper, this distribution and its main properties are examined, and the parameters are estimated using several estimation methods. In addition, a simulation study is done for different sample sizes. The performance of the proposed model is illustrated through two real-world applications: component failure times and COVID-19 mortality. Moreover, the value-at-risk (VaR), tail value-at-risk (TVaR), peaks over a random threshold VaR (PORT-VaR), the mean of order P ((Formula presented.)) analysis, and optimal order of P due to the true mean value can help identify and characterize critical events or outliers in failure events and COVID-19 death data across different counties. Finally, the PORT-VaR estimators are provided under a risk analysis for both applications.
AB - The weighted flexible Weibull distribution focuses on its unique point of flaunting a bathtub-shaped hazard rate, characterized by an initial increase followed by a drop over time. This property plays a major role in reliability analysis. In this paper, this distribution and its main properties are examined, and the parameters are estimated using several estimation methods. In addition, a simulation study is done for different sample sizes. The performance of the proposed model is illustrated through two real-world applications: component failure times and COVID-19 mortality. Moreover, the value-at-risk (VaR), tail value-at-risk (TVaR), peaks over a random threshold VaR (PORT-VaR), the mean of order P ((Formula presented.)) analysis, and optimal order of P due to the true mean value can help identify and characterize critical events or outliers in failure events and COVID-19 death data across different counties. Finally, the PORT-VaR estimators are provided under a risk analysis for both applications.
KW - COVID-19
KW - flexible Weibull
KW - mean of order P
KW - peaks over a random threshold for value-at-risk estimation
KW - risk analysis
KW - true mean value
UR - http://www.scopus.com/inward/record.url?scp=105003693959&partnerID=8YFLogxK
U2 - 10.3390/mca30020042
DO - 10.3390/mca30020042
M3 - Article
AN - SCOPUS:105003693959
SN - 1300-686X
VL - 30
JO - Mathematical and Computational Applications
JF - Mathematical and Computational Applications
IS - 2
M1 - 42
ER -