MIXTURES OF TAILS IN CLUSTERED AUTOMOBILE COLLISION CLAIMS

Knowledge of the tail shape of claim distributions provides important actuarial information. This paper discusses how two techniques commonl y used in assessing the most appropriate underlying distribution can b e 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, no t always capable to discriminate among non-nested classes of distribut ions. Extremal value theory offers an attractive tool to overcome this problem. It shows that a much larger set of distributions is nested i n their tails by the so-called tail parameter. This paper shows that b oth estimation strategies can be usefully combined when the data gener ating process is characterized by strong clustering in time and size. We find that the extreme value theory is a useful starting point in de tecting the appropriate distribution class. Once that has been achieve d, the likelihood-based EM-algorithm is proposed to capture the cluste ring phenomena. Clustering is particularly pervasive in actuarial data . An empirical application to a four-year data set of Dutch automobile collision claims is therefore used to illustrate the approach.