A Normal-Gamma copula for dependence modeling in collective risk models

Abstract This paper introduces a new copula family and a corresponding statistical methodology for modeling the dependence between claim frequency and average severity in the collective risk model (CRM). Existing copula-based approaches often struggle to capture the intrinsic dependence structure between these variables. To address this limitation, we propose the Normal-Gamma (NG) copula, which is derived from the NG distribution and naturally exhibits a decreasing conditional variance property. This property aligns well with the empirical characteristics of claim frequency and average severity, making the NG copula particularly suitable for CRM applications. The effectiveness of the proposed copula is demonstrated through numerical studies and real data analysis.