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“Toward a Unified Approach to Fitting Loss Models”, Stuart Klugman and Jacques Rioux, January 2006

1. OVERVIEW The paper by Professors Klugman and Rioux provides a unified approach to fitting loss models. We agree with the authors on the four points needed to identify an appropriate model: selecting candidate distributions, estimating parameters, evaluating models, and determining which model fits best. To underscore the importance of their work, we would like to consider a more general framework by discussing how an actuary would introduce explanatory variables, also known as covariates, thus employing a regression modeling framework. Klugman, Panjer, and Willmot (2004) present the use of covariates using the Cox proportional hazards, a type of regression model for lifetime data. In this discussion we focus our attention on regression models with heavy-tailed distributions. In practice, actuaries often encounter situations where the measurements of interest are related to other factors. However, implicit in the usual regression routines is the requirement of approximate normality—hardly satisfactory for loss data with heavy tails. One solution that has been widely used in the literature to deal with the skewness is to apply a logarithmic transformation of the dependent variable Y and then apply the ordinary least square (OLS) on ln(Y). A second is to use generalized linear models (GLMs), which provide a natural way to include covariates in the models. A third approach is