  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.
