Risk Analysis and Estimation of a Bimodal Heavy-Tailed Burr XII Model in Insurance Data: Exploring Multiple Methods and Applications

Actuarial risks can be analyzed using heavy-tailed distributions, which provide adequate risk assessment. Key indicators, such as value-at-risk, tailed-value-at-risk (conditional tail expectation), tailed-variance, tailed-mean-variance, and mean excess loss function, are commonly used to evaluate exposure levels. In this study, we analyze actuarial these five calculated four different estimation methods: maximum likelihood, ordinary least square, weighted Cramer-Von-Mises. To achieve our main goal, introduce study a new distribution. Monte Carlo simulations assess the performance of all methods. We two real-life datasets with applications compare classical methods demonstrate importance proposed model, evaluated via likelihood method. Finally, abovementioned indicators based on bimodal insurance claim payments data.