INSURANCE RISK CLASSIFICATION WITH NEGATIVE BINOMIAL DISTRIBUTION

Abstract

Risk classification is the process of statistical modeling that classifies risks into cross-classified classes, characterized by
the rating factors. In this paper, risk classification is applied to estimate claim frequency rates, expressed in terms of claim
count per exposure unit. The Poisson regression model has been widely used to analyze claim frequency rates in the recent
years. However, under the Poisson model, the mean and variance is assumed to be equal within classes, i.e., homogeneous
rates. In this paper, the Negative Binomial regression model is suggested to deal with heterogeneous rates. In addition, the
measures for goodness-of-fit of the model, namely the Pearson chi-square, deviance, and likelihood ratio test, are also
discussed. Finally, the procedure for estimation of parameters, namely the Iteratively Weighted Least Squares (IWLS), is
also shown. In this paper, the models are fitted and tested on two types of claim data; Canadian private automobile liability
insurance and Malaysian private automobile own damage insurance.