Asymptotic Laws for Upper and Strong Record Values in the Extreme Domain of Attraction and Beyond

Gane Samb Lo, Mohammad Ahsanullah, Moumouni Diallo, Modou Ngom

Abstract

Asymptotic laws of records values have usually been investigated as limits in type. In this paper, we use functional representations of the tail of cumulative distribution functions in the extreme value domain of attraction to directly establish asymptotic laws of records value, not necessarily as limits in type and their rates of convergences. Results beyond the extreme value value domain are provided. Explicit asymptotic laws concerning very usual laws and related rates of convergence are listed as well. Some of these laws are expected to be used in fitting distribution.

Keywords

record values and record times; normal Asymptotic theory; extreme value theory; generalized extreme value distributions} \ams{AMS classification codes

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