The Weighted Flexible Weibull Model: Properties, Applications, and Analysis for Extreme Events

Abstract

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. © 2025 by the authors.