A smooth hazard-blend composite model for heavy-tailed loss data: Bayesian and frequentist comparisons with applications in actuarial science

Accurate modeling of the loss distributions is crucial for solvency capital assessment and reinsurance pricing. Conventional single-component models fail to capture the dual nature of insurance data, which consists of a high-frequency body and a heavy tails of extreme losses. This paper introduces a novel composite Weibull–Pareto model with a smooth logistic transition in the hazard rates by avoiding discontinuities. We compare frequentist (maximum likelihood) and the Bayesian estimation using weakly informative and empirical priors to assess parameter uncertainty and tail risk. Using the canonical Danish Fire Insurance dataset, the results indicate that Bayesian inference delivers superior predictive performance and conservative estimates of the extreme tail-risk measures such as Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR). Maximum likelihood estimates appear overly optimistic, whereas the Bayesian methods yield more credible capital and reinsurance payouts, particularly for the catastrophic layers. The proposed hazard blend offers a robust framework for actuaries, enhancing both methodological rigor and practical applicability in the composite loss modeling.