1112.2965 (Florian Angeletti et al.)

Renormalization flow for extreme value statistics of random variables
raised to a varying power    [PDF]

Florian Angeletti, Eric Bertin, Patrice Abry

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.

View original: http://arxiv.org/abs/1112.2965