In this paper, we propose two important extensions to cluster-weighted models (CWMs).
First, we extend CWMs to have generalized cluster-weighted models (GCWMs) by allowing
modeling of non-Gaussian distribution of the continuous covariates, as they frequently
occur in insurance practice. Secondly, we introduce a zero-inﬂated extension
of GCWM (ZI-GCWM) for modeling insurance claims data with excess zeros coming
from heterogenous sources. Additionally, we give two expectation-optimization (EM)
algorithms for parameter estimation given the proposed models. An appropriate simulation
study shows that, for various settings and in contrast to the existing mixture-based
approaches, both extended models perform well. Finally, a real data set based on French
auto-mobile policies is used to illustrate the application of the proposed extensions.