Composite and Mixture Distributions for Heavy-Tailed Data—An Application to Insurance Claims

Walena Anesu Marambakuyana and Sandile Charles Shongwe ()
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Walena Anesu Marambakuyana: Department of Mathematical Statistics and Actuarial Science, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9301, South Africa
Sandile Charles Shongwe: Department of Mathematical Statistics and Actuarial Science, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9301, South Africa

Mathematics, 2024, vol. 12, issue 2, 1-23

Abstract: This research provides a comprehensive analysis of two-component non-Gaussian composite models and mixture models for insurance claims data. These models have gained attraction in actuarial literature because they provide flexible methods for curve-fitting. We consider 256 composite models and 256 mixture models derived from 16 popular parametric distributions. The composite models are developed by piecing together two distributions at a threshold value, while the mixture models are developed as convex combinations of two distributions on the same domain. Two real insurance datasets from different industries are considered. Model selection criteria and risk metrics of the top 20 models in each category (composite/mixture) are provided by using the ‘single-best model’ approach. Finally, for each of the datasets, composite models seem to provide better risk estimates.

Keywords: claims; composite models; Danish fire loss; heavy-tailed; loss distribution; mixture models; risk measures; single best model approach; skewed (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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