Estimating the Heavy Tail Index from Scaling Properties
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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.
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- M. E. Crovella, M. S. Taqqu, and A. Bestavros, “Heavy-tailed probability distributions in the world wide web,” In A Practical Guide To Heavy Tails, chapter 1, pp. 3–25, Chapman & Hall, New York, 1998.Google Scholar
- W. Feller, An Introduction to Probability Theory and its Applications, volume II, John Wiley and Sons, second edition, 1971.Google Scholar
- B. M. Hill, “A simple general approach to inference about the tail of a distribution,'' The Annals of Statistics vol. 3 pp. 1163–1174, 1975.Google Scholar
- G. Samorodnitsky and Murad S. Taqqu, Stable Non-Gaussian Random Processes Stochastic Modeling, Chapman and Hall: New York, 1994.Google Scholar
- V. M. Zolotarev, “One-dimensional Stable Distributions,” Translations of mathematical monographs, vol. 65 American Mathematical Society, 1986.Google Scholar