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.
