Abstract:

Finding appropriate distributions for describing the claim amounts in insurance is critical. The main objective of this article is to model insurance claims using a set of flexible skewed and mixture probability density functions, and to test how well the chosen statistical distribution fits the claims. Our results indicate that skewt and alphaskew Laplace distributions are able to describe unimodal claim distributions accurately whereas scale mixture of skewnormal and skewt distributions are better alternatives to both unimodal and bimodal conventional distributions such as skewnormal, alpha skewnormal, mixture of normals. In addition to goodnessoffit tests, we calculated tail risk measures such as value at risk and tail value at risk as judgment criteria to assess the fitness of the probability density functions.
