Mixtures of tails in clustered automobile collision claims

Abstract

Knowledge of the tail shape of claim distributions provides important actuarial information. This paper discusses how two techniques commonly used in assessing the most appropriate underlying distribution can be usefully combined. The maximum likelihood approach is theoretically appealing since it is preferable to many other estimators in the sense of best asymptotic normality. Likelihood based tests are, however, not always capable to discriminate among non-nested classes of distributions. Extremal value theory offers an attractive tool to overcome this problem. It shows that a much larger set of distributions is nested in their tails by the so-called tail parameter. This paper shows that b..