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December, 1983 Estimating the Stable Index $\alpha$ in Order to Measure Tail Thickness: A Critique
William H. DuMouchel
Ann. Statist. 11(4): 1019-1031 (December, 1983). DOI: 10.1214/aos/1176346318


Stable laws are often fit to outlier-prone data and, if the index $\alpha$ is estimated to be much less than two, then the normal law is rejected in favor of an infinite-variance stable law. This paper derives the theoretical properties of such a procedure. When the true distribution is stable, the distribution of the m.l.e. of $\alpha$ is non-regular if $\alpha = 2$. When the true distribution is not stable, the estimate of $\alpha$ is not a robust measure of the rate of decrease of the tail probabilities. A more robust procedure is developed, and a statistic for describing and comparing the tail-shapes of arbitrary samples is proposed.


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William H. DuMouchel. "Estimating the Stable Index $\alpha$ in Order to Measure Tail Thickness: A Critique." Ann. Statist. 11 (4) 1019 - 1031, December, 1983.


Published: December, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0547.62022
MathSciNet: MR865342
Digital Object Identifier: 10.1214/aos/1176346318

Primary: 62F25
Secondary: 62G99

Rights: Copyright © 1983 Institute of Mathematical Statistics


Vol.11 • No. 4 • December, 1983
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