, Volume 9, Issue 2, pp 131–149 | Cite as

Tail approximations to the density function in EVT



Let X 1, X 2, ...,X n be independent identically distributed random variables with common distribution function F, which is in the max domain of attraction of an extreme value distribution, i.e., there exist sequences a n > 0 and b n ∈ ℝ such that the limit of \(P(a_n^{-1}(\max_{1\leq i\leq n}X_i-b\!_n)\leq x)\) exists. Assume the density function f (of F) exists. We obtain an uniformly weighted approximation to the tail density function f, and an uniformly weighted approximation to the tail density function of \(P(a_n^{-1}(\max_{1\leq i\leq n}X_i-b\!_n)\leq x)\) under some second order condition.


Tail approximation Density function Maximum Extreme value distribution Differentiable domain of attraction 

AMS 2000 Subject Classifications

62G32 60G70 


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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of Mathematical Statistics and Actuarial ScienceUniversity of BernBernSwitzerland

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