A SKEW-NORMAL APPROXIMATION FOR POISSON- GAMMA CLAIM DISTRIBUTION

Abstract

The Normal approximation is a commonly used method by insurance companies to estimate the distribution of claims. However, the distribution of insurance claims often exhibits significant skewness, which cannot be adequately accommodated by the Normal approximation. This study aims to propose an alternative approximation method that performs better than the Normal approximation. Built upon the presumption that the actual distribution of claims follows the Poisson-Gamma distribution, this research investigates the effectiveness of two approximation approaches. The comparison is conducted using mean-squared error (MSE) analysis, which assesses the extent to which these approaches approximate the actual distribution of claims in a simulation scenario. The results show that the Skew-Normal approximation outperforms the Normal approximation in terms of estimating the distribution of claims. Finally, the Skew-Normal distribution was developed as a solution to the problem of skewness in insurance claim distributions and to improve estimation accuracy.