# Modeling Frequency and Severity of Claims with the Zero-Inflated Generalized Cluster-Weighted Models

## TL;DR

This paper introduces zero-inflated generalized cluster-weighted models to better analyze insurance claims data with excess zeros and non-Gaussian covariates, improving modeling accuracy.

## Contribution

The paper extends cluster-weighted models to handle non-Gaussian covariates and excess zeros in insurance data, with new EM algorithms for parameter estimation.

## Key findings

- Both models perform well in simulations.
- Models effectively handle excess zeros.
- Application to real data demonstrates practical utility.

## Abstract

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.