Renormalization flow for extreme value statistics of random variables raised to a varying power Article - Janvier 2012

Florian Angeletti, Eric Bertin, Patrice Abry

Florian Angeletti, Eric Bertin, Patrice Abry, « Renormalization flow for extreme value statistics of random variables raised to a varying power  », Journal of Physics A : Mathematical and Theoretical, janvier 2012, p. 115004. ISSN 1751-8113

Abstract

Using a renormalization approach, we study the asymptotic limit distribution of the maximum value in a set of independent and identically distributed random variables raised to a power q(n) that varies monotonically with the sample size n. Under these conditions, a non-standard class of max-stable limit distributions, which mirror the classical ones, emerges. Furthermore a transition mechanism between the classical and the non-standard limit distributions is brought to light. If q(n) grows slower than a characteristic function q*(n), the standard limit distributions are recovered, while if q(n) behaves asymptotically as k.q*(n), non-standard limit distributions emerge.

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