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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

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.

Authors who are presenting talks have a * after their name.

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