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

Bruce M Hill · 1975
DOI: 10.1214/aos/1176343247

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−αG(y)=1−Cy−αG(y) = 1 - Cy\textasciicircum-\textbackslashalpha\ for large yyy. 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.

Reference

Bruce M Hill “A Simple General Approach to Inference About the Tail of a Distribution” (1975) DOI: 10.1214/aos/1176343247

@Article{hill1975,
  title = {A Simple General Approach to Inference About the Tail of a Distribution},
  volume = {3},
  issn = {0090-5364, 2168-8966},
  url = {https://projecteuclid.org/euclid.aos/1176343247},
  doi = {10.1214/aos/1176343247},
  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−αG(y)=1−Cy−αG(y) = 1 - Cy\textasciicircum\-\textbackslashalpha\ for large yyy. 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.},
  language = {EN},
  number = {5},
  urldate = {2020-06-27},
  journal = {Annals of Statistics},
  author = {Hill, Bruce M},
  month = {sep},
  year = {1975},
  mrnumber = {MR378204},
  zmnumber = {0323.62033},
  note = {Publisher: Institute of Mathematical Statistics},
  keywords = {Bayesian inference, order statistics, Tail of distribution},
  pages = {1163--1174}
}