The normal distribution comes as a first choice when fitting real data, but it may not be suitable if the assumed distribution deviates from normality. Flexible skewed distributions are capable of including skewness and taking into account multimodality. They may be applied to find appropriate distributions for describing the claim amounts in insurance. The objective is to model insurance claims using a set of flexible skewed and mixture probability distributions, and to test how well they fit the claims. Results indicate the skew-t distribution and alpha-skew Laplace distribution are able to describe unimodal claims accurately, whereas scale mixture of skew-normal and skew-t distributions are better alternatives to both unimodal and bimodal conventional distributions such as skew-normal, alpha skew-normal, and mixture of normal distributions. The tail risk measures such as value at risk and tail value at risk are estimated as judgment criteria to assess the fitness of the models.
Leinwander, A. J., & Aziz, M. A. (2018). Modeling Insurance Claims Using Flexible Skewed and Mixture Probability Distributions. Journal of Modern Applied Statistical Methods, 17(1), eP2467. doi: 10.22237/jmasm/1525133100