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On large deviation for extremes

✍ Scribed by Holger Drees; Laurens de Haan; Deyuan Li

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
224 KB
Volume
64
Category
Article
ISSN
0167-7152

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✦ Synopsis

Recently, a weighted approximation for the tail empirical distribution function has been developed (Approximations to the tail empirical distribution function with application to testing extreme value conditions. preprint, submitted for publication). We show that the same result can also be used to improve a known uniform approximation of the distribution of the maximum of a random sample. From this a general result about large deviations of this maximum is derived. In addition, the relationship between two second-order conditions used in extreme value theory is clariΓΏed.

πŸ“œ SIMILAR VOLUMES

On large deviations
On large deviations
✍ V. A. Statulevičius πŸ“‚ Article πŸ“… 1966 πŸ› Springer 🌐 English βš– 431 KB
Large Deviations for Quicksort
Large Deviations for Quicksort
✍ C.J.H. McDiarmid; R.B. Hayward πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 300 KB

Let Q be the random number of comparisons made by quicksort in sorting n n distinct keys when we assume that all n! possible orderings are equally likely. Known results concerning moments for Q do not show how rare it is for Q to n n make large deviations from its mean. Here we give a good approxima