Estimation of quantiles of the maximum of N observations

1 June 1987

journal article
research article
Published by Oxford University Press (OUP) in Biometrika

Vol. 74 (2) , 347-354
https://doi.org/10.1093/biomet/74.2.347

Abstract

Given independent and identically distributed random variables from an unknown distribution F, we want to estimate quantiles of F^N. Using asymptotic extreme-value theory, two parametric approximations to F^N are considered and approximate maximum likelihood estimates are obtained. Conditions for consistency and asymptotic normality of these estimates are given, and properties of the estimates are obtained through a small simulation study.

Keywords

EXTREME-VALUE THEORY: GENERALIZED EXTREME-VALUE DISTRIBUTION
GENERALIZED PARETO DISTRIBUTION
MAXIMUM LIKELIHOOD ESTIMATION
QUANTILE

This publication has 2 references indexed in Scilit:

Modelling Excesses over High Thresholds, with an Application
Published by Springer Nature ,1984
Threshold Methods for Sample Extremes
Published by Springer Nature ,1984