Estimating the Heavy Tail Index from Scaling Properties

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Abstract

This paper deals with the estimation of the tail index α for empirical heavy-tailed distributions, such as have been encountered in telecommunication systems. We present a method (called the “scaling estimator”) based on the scaling properties of sums of heavy-tailed random variables. It has the advantages of being nonparametric, of being easy to apply, of yielding a single value, and of being relatively accurate on synthetic datasets. Since the method relies on the scaling of sums, it measures a property that is often one of the most important effects of heavy-tailed behavior. Most importantly, we present evidence that the scaling estimator appears to increase in accuracy as the size of the dataset grows. It is thus particularly suited for large datasets, as are increasingly encountered in measurements of telecommunications and computing systems.