A new losses (revenues) probability model with entropy analysis, applications and case studies for value-at-risk modeling and mean of order-P analysis

This study introduces the Inverse Burr-X Burr-XII (IBXBXII) distribution as a novel approach for handling asymmetric-bimodal claims and revenues. It explores the distribution's statistical properties and evaluates its performance in three contexts. The analysis includes assessing entropy, highlighting the distribution's significance in various fields, and comparing it to rival distributions using practical examples. The IBXBXII model is then applied to analyze risk indicators in actuarial data, focusing on bimodal insurance claims and income. Simulation analysis shows its preference for right-skewed data, making it suitable for mathematical modeling and actuarial risk assessments. The study emphasizes the IBXBXII model's versatility and effectiveness, suggesting it as a flexible framework for actuarial data analysis, particularly in cases of large samples and right-skewed data.