Open Access
February, 1985 On Domains of Uniform Local Attraction in Extreme Value Theory
T. J. Sweeting
Ann. Probab. 13(1): 196-205 (February, 1985). DOI: 10.1214/aop/1176993075


An absolutely continuous distribution $F$ is said to be in the domain of uniform local attraction of the absolutely continuous distribution $H$ if the density of the normalized maximum of an independent sample of size $n$ converges locally uniformly to the density of $H$ as $n \rightarrow \infty$. Under the sole restriction that $F$ is eventually increasing, the domains of uniform local attraction to the three types of extreme value distribution are shown to be characterized by the usual Von Mises' conditions. The equivalent form of conditions used here greatly simplifies and shortens proofs of known results. In particular, $L_p$ convergence and convergence of the $k$ upper sample extremes are investigated and extensions to known results derived.


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T. J. Sweeting. "On Domains of Uniform Local Attraction in Extreme Value Theory." Ann. Probab. 13 (1) 196 - 205, February, 1985.


Published: February, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0566.60022
MathSciNet: MR770637
Digital Object Identifier: 10.1214/aop/1176993075

Primary: 60F05
Secondary: 60F25

Keywords: $L_p$ convergence , Domains of uniform local attraction , Extreme value theory , slow variation

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 1 • February, 1985
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