How to Make a Hill Plot

An abundance of high quality data sets requiring heavy tailed models necessitates reliable methods of estimating the shape parameter governing the degree of tail heaviness. The Hill estimator is a popular method for doing this but its practical use is encumbered by several diiculties. We show that an alternative method of plotting Hill estimator values is more revealing than the standard method unless the underlying data comes from a Pareto distribution. 1. Introduction It is becoming increasingly common to encounter large, high quality data sets for which appropriate models require heavy tailed distributions. Examples abound from the elds of insurance By a heavy tailed distribution we mean a distribution F, assumed for convenience to concen