Open Access
September, 1975 A Simple General Approach to Inference About the Tail of a Distribution
Bruce M. Hill
Ann. Statist. 3(5): 1163-1174 (September, 1975). DOI: 10.1214/aos/1176343247


A simple general approach to inference about the tail behavior of a distribution is proposed. It is not required to assume any global form for the distribution function, but merely the form of behavior in the tail where it is desired to draw inference. Results are particularly simple for distributions of the Zipf type, i.e., where $G(y) = 1 - Cy^{-\alpha}$ for large $y$. The methods of inference are based upon an evaluation of the conditional likelihood for the parameters describing the tail behavior, given the values of the extreme order statistics, and can be implemented from both Bayesian and frequentist viewpoints.


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Bruce M. Hill. "A Simple General Approach to Inference About the Tail of a Distribution." Ann. Statist. 3 (5) 1163 - 1174, September, 1975.


Published: September, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0323.62033
MathSciNet: MR378204
Digital Object Identifier: 10.1214/aos/1176343247

Primary: 62F99

Keywords: Bayesian inference , order statistics , tail of distribution

Rights: Copyright © 1975 Institute of Mathematical Statistics

Vol.3 • No. 5 • September, 1975
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