Severity Distributions for GLMs: Gamma or Lognormal? Evidence from Monte Carlo Simulations

Insurance claim costs have been found in numerous studies to be positive and usually positively skewed with variance often proportional to the mean squared. In practice, the gamma and lognormal distributions are the ones with those desired properties most widely used. Most actuarial research in GLMs also report results from normal distributions as a comparison. In this study, we apply Monte Carlo simulation techniques to examine the unbiasedness and stability of the GLM classification relativities assuming gamma, lognormal, and normal distributions. We find that the gamma distribution provides better predictive accuracy and efficiency.