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Activity Number: 550
Type: Contributed
Date/Time: Wednesday, August 3, 2016 : 10:30 AM to 12:20 PM
Sponsor: Business and Economic Statistics Section
Abstract #321385
Title: Modeling Insurance Claims Using Skewed and Mixture Probability Distributions
Author(s): Mohammad Aziz* and Aaron Leinwander
Companies: University of Wisconsin - Eau Claire and Security Health Plan
Keywords: Skew-normal distribution ; Flexible skewed-distributions ; Mixture distributions ; Finite mixture of scale mixture of skew normal-distribution ; Value at risk ; Tail value at risk
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 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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