A Bayesian approach for modeling heavy tailed insurance claim data based on the contaminated lognormal distribution

Mahsa Salajegheh, Mehdi Jabbari Nooghabi () and Kheirolah Okhli
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Mahsa Salajegheh: Ferdowsi University of Mashhad
Mehdi Jabbari Nooghabi: Ferdowsi University of Mashhad
Kheirolah Okhli: Ferdowsi University of Mashhad

METRON, 2025, vol. 83, issue 2, No 3, 213-234

Abstract: Abstract Recently, analysis of the insurance claims data with outliers has achieved considerable attention for insurance industries. In this regard, this paper introduces a methodology based on the contaminated lognormal distribution as an appropriate platform for analyzing insurance data with some levels of heavy tailed points. The Bayesian approach for computing the parameter estimates and the insurance premium is studied. In order to investigate the performance of the proposed methodology, some simulation studies are conducted by implementing the Gibbs sampler. We demonstrate that the proposed model is an appropriate and preferred model for dealing with the data with and without heavy tailed points. Finally, two examples of real insurance claim data have been analyzed to illustrate how well the contaminated lognormal distribution with Bayesian parameter inference works. Also, this paper studies that the proposed model outperforms the other existing models in the literature.

Keywords: Heavy tailed data; Outliers; Insurance claims data; Insurance premium; Contaminated lognormal distribution; Mixture model; Heavy tailed distribution; Bayesian analysis; Gibbs sampler (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s40300-025-00288-9

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