A discrete claims-model for the inflated and over-dispersed automobile claims frequencies data: Applications and actuarial risk analysis

Abstract

This paper showcases the effectiveness of the discrete generalized Burr-Hatke distribution in analyzing insurance claims data, specifically focusing on scenarios with over-dispersed and zero-inflated claims. Key contributions include presenting foundational statistical theories with mathematical proofs to enrich the paper’s mathematical and statistical aspects. Through the application of this discrete distribution, the study conducted a thorough risk analysis across five diverse sets of insurance claims data, evaluating critical risk indicators at specified quantiles. These indicators provided detailed insights into potential losses across different risk levels, supporting effective risk management strategies. The research emphasizes the importance of selecting appropriate probability distributions when analyzing zero-inflated data, as commonly observed in insurance claims. The discrete distribution accommodated these unique data characteristics and facilitated a robust analysis of risk metrics, enhancing the accuracy of potential loss assessments and reducing associated uncertainties. Furthermore, the study highlights the practical relevance of the discrete distribution in addressing specific challenges inherent to insurance claims data. By leveraging this distribution, insurers and risk analysts can improve their risk modeling capabilities, leading to more informed decision-making and enhanced financial exposure management.