Prediction region for average claim occurrence rate and average claim size in motor insurance

Abstract

The third-party motor insurance data from Sweden for 1977 described by Andrews and Herzberg in 1985 contain average claim occurrence rate (Pc) , average claim size (Ca) for category of vehicles specified by the kilometres travelled per year (K), geographical zone (Z), no claims bonus (B) and make of car (M). The categorical variables Z and M may first be represented respectively by the vectors (Z1, Z2, … , Z6) and (M1, M2, … , M8) of binary variables. The variable (Pc, Ca) is next modelled to be dependent on X∗ = (K, Z1, Z2, … , Z6, B, M1, M2, … , M8) via a conditional distribution which is derived from an 18-dimensional powernormal distribution. From the conditional distribution, a prediction region for (Pc, Ca) can be obtained to provide useful information on the possible ranges of average claim occurrence rate and average claim size for a given category of vehicles.