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

<jats:p>The third-party motor insurance data from Sweden for 1977 described by Andrews and Herzberg in 1985 contain average claim occurrence rate (P<jats:sub>c</jats:sub>) , average claim size (C<jats:sub>a</jats:sub>) 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 (Z<jats:sub>1</jats:sub>, Z<jats:sub>2</jats:sub>, … , Z<jats:sub>6</jats:sub>) and (M<jats:sub>1</jats:sub>, M<jats:sub>2</jats:sub>, … , M<jats:sub>8</jats:sub>) of binary variables. The variable (P<jats:sub>c</jats:sub>, C<jats:sub>a</jats:sub>) is next modelled to be dependent on X<jats:sup>∗</jats:sup> = (K, Z<jats:sub>1</jats:sub>, Z<jats:sub>2</jats:sub>, … , Z<jats:sub>6</jats:sub>, B, M<jats:sub>1</jats:sub>, M<jats:sub>2</jats:sub>, … , M<jats:sub>8</jats:sub>) via a conditional distribution which is derived from an 18-dimensional powernormal distribution. From the conditional distribution, a prediction region for (P<jats:sub>c</jats:sub>, C<jats:sub>a</jats:sub>) 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.</jats:p>