A dependent and censored first hitting-time model with compound Poisson processes

We consider a bivariate first hitting-time model in which durations are the crossing times of dependent compound Poisson processes with fixed thresholds. The identifiability of the model is discussed, and likelihood estimators of the model parameters are proposed. We obtain the asymptotic properties of the estimators and underline their finite sample performance with a simulation study on synthetic data. The practical applicability of our approach is demonstrated by an application using data from patients suffering from mushroom poisoning. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s10985-026-09705-1.