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Abstract:
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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 skew-t and alpha-skew Laplace distributions are able to describe unimodal claim distributions 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, mixture of normals. In addition to goodness-of-fit 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.
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