Fitting insurance claims to skewed distributions: Are the skew-normal and skew-student good models?

This paper analyzes whether the skew-normal and skew-student distributions recently discussed in the finance literature are reasonable models for describing claims in property-liability insurance. We consider two well-known datasets from actuarial science and fit a number of parametric distributions to these data. Also the non-parametric transformation kernel approach is considered as a benchmark model. We find that the skew-normal and skew-student are reasonably competitive compared to other models in the literature when describing insurance data. In addition to goodness-of-fit tests, tail risk measures such as value at risk and tail value at risk are estimated for the datasets under consideration. ► The skew-normal and skew-student distributions are recently discussed in finance literature. ► Are these reasonable models for describing claims in property-liability insurance? ► We empirically apply these two distributions to two well known datasets. ► We consider various goodness of fit tests and estimate tail risk measures. ► Result: the two models are reasonably good compared to other models used in literature.