Overdispersed and Zero-Truncated Count Models for Hospitality Insurance Claim Frequencies

Abstract

Insurance claim frequencies are commonly modeled by Poisson regression, although the equidispersion assumption is often violated in real insurance portfolios. This paper studies count regression models for hospitality insurance claim counts under overdispersion and strictly positive sampling. We formulate the Poisson model as a benchmark and motivate the negative binomial model through its conditional mean-variance structure and Poisson–gamma mixture representation. Due to positive-count sampling, zero-truncated extensions are also contemplated. The empirical analysis is based on multi-year hospitality insurance claim data and statistically compares the benchmark, negative binomial along with Conway–Maxwell–Poisson, geometric, and zero-truncated specifications using dispersion diagnostics, likelihood-based criteria, and cross validation. The result shows that the negative binomial substantially improves the Poisson benchmark reducing the cross validated AIC by 1,003.46 on average. Among the extended models, the zero-truncated negative binomial model achieves the best likelihood-based fit, supported by the lowest AIC and BIC. These findings indicate that both unobserved heterogeneity and zero-truncation are crucial features of hospitality insurance claim frequencies.