A Comparison between Skew-logistic and Skew-normal Distributions

Abstract

Skew distributions are reasonable models for describing claims in property-liability insurance. We consider two well-known datasets from actuarial science and fit skew-normal and skew-logistic distributions to these dataset. We find that the skew-logistic distribution is reasonably competitive compared to skew-normal in the literature when describing insurance data. The value at risk and tail value at risk are estimated for the dataset under consideration. Also, we compare the skew distributions via Kolmogorov-Smirnov goodness-of-fit test, log-likelihood criteria and AIC.