Super-Slowly Varying Functions in Extreme Value Theory
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1978 · Volume 40 · Issue 2
DOI: 10.1111/j.2517-6161.1978.tb01664.x
Abstract
Large-deviation limit theorems for maxima of random samples in the domain of attraction of the extreme value distribution Φαare studied, motivated by examination of an approximation used in the statistical analysis of large observations. The large-deviation property is shown to be equivalent to a strengthened form of slow variation condition, called here super-slow variation, on the tail of the distribution of a single observation. Various conditions for super-slow variation are discussed and Karamata's representation for slowly varying functions is extended to a wide class of super-slowly varying functions.
Keywords
large deviation limits, slow variation, extreme values
Enable JavaScript for citation tools and additional paper interactions.