Robust Claim Frequency Modeling Through Phase-Type Mixture-of-Experts Regression

31 Pages Posted: 30 Dec 2022

See all articles by Martin Bladt

Martin Bladt

University of Copenhagen

Jorge Yslas

University of Liverpool


This paper addresses the problem of modeling loss frequency using regression when the counts have a non-standard distribution. We propose a novel approach based on mixture-of-experts specifications on discrete-phase type distributions. Compared to continuous phase-type counterparts, our approach offers fast estimation via expectation-maximization, making it more feasible for use in real-life scenarios. Our model is both robust and interpretable in terms of risk classes, and can be naturally extended to the multivariate case through two different constructions. This avoids the need for ad-hoc multivariate claim count modeling. Overall, our approach provides a more effective solution for modeling loss frequency in non-standard situations.

Keywords: discrete phase-type distributions, regression modelling, claim count distributions

Suggested Citation

Bladt, Martin and Yslas, Jorge, Robust Claim Frequency Modeling Through Phase-Type Mixture-of-Experts Regression. Available at SSRN: or

Martin Bladt (Contact Author)

University of Copenhagen ( email )

Nørregade 10
Copenhagen, DK-1165

Jorge Yslas

University of Liverpool ( email )

Chatham Street
Brownlow Hill
Liverpool, L69 7ZA
United Kingdom

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