## Annals of Statistics

### A Simple General Approach to Inference About the Tail of a Distribution

Bruce M. Hill

#### Abstract

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.

#### Article information

Source
Ann. Statist., Volume 3, Number 5 (1975), 1163-1174.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343247

Digital Object Identifier
doi:10.1214/aos/1176343247

Mathematical Reviews number (MathSciNet)
MR378204

Zentralblatt MATH identifier
0323.62033

JSTOR
links.jstor.org

Subjects
Primary: 62F99: None of the above, but in this section

#### Citation

Hill, Bruce M. A Simple General Approach to Inference About the Tail of a Distribution. Ann. Statist. 3 (1975), no. 5, 1163--1174. doi:10.1214/aos/1176343247. https://projecteuclid.org/euclid.aos/1176343247