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Estimating the Heavy Tail Index from Scaling Properties

Author

Listed:
  • Mark E. Crovella

    (Boston University)

  • Murad S. Taqqu

    (Boston University)

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.

Suggested Citation

  • Mark E. Crovella & Murad S. Taqqu, 1999. "Estimating the Heavy Tail Index from Scaling Properties," Methodology and Computing in Applied Probability, Springer, vol. 1(1), pages 55-79, July.
    • Handle: RePEc:spr:metcap:v:1:y:1999:i:1:d:10.1023_a:1010012224103
    DOI: 10.1023/A:1010012224103
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    Cited by:

    1. Cirillo, Pasquale & Hüsler, Jürg, 2009. "On the upper tail of Italian firms’ size distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1546-1554.
    2. Shaler Stidham, 2002. "Analysis, Design, and Control of Queueing Systems," Operations Research, INFORMS, vol. 50(1), pages 197-216, February.
    3. Paulo M.M. Rodrigues & João Nicolau, 2015. "A New Regression-Based Tail Index Estimator: An Application to Exchange Rates," Working Papers w201514, Banco de Portugal, Economics and Research Department.
    4. Søren Asmussen & Jaakko Lehtomaa, 2017. "Distinguishing Log-Concavity from Heavy Tails," Risks, MDPI, vol. 5(1), pages 1-14, February.
    5. Rimas Norvaiša & Donna Mary Salopek, 2002. "Estimating the p-Variation Index of a Sample Function: An Application to Financial Data Set," Methodology and Computing in Applied Probability, Springer, vol. 4(1), pages 27-53, March.

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