A pedagogical account of some aspects of extreme value statistics (EVS) is presented from the
somewhat non-standard viewpoint of large deviation theory. We address the following problem: given a
set of N independent and identically distributed (i.i.d.) random variables ##IMG##
[http://ej.iop.org/images/0143-0807/36/5/055037/ejp518115ieqn1.gif] {${{X}_{1},ldots ,{X}_{N}}$}
drawn from a parent probability density function (pdf) ##IMG##
[http://ej.iop.org/images/0143-0807/36/5/055037/ejp518115ieqn2.gif] {$p(x)$} , what is the
probability that the maximum value of the set ##IMG##
[http://ej.iop.org/images/0143-0807/36/5/055037/ejp518115ieqn3.gif]
{${X}_{mathrm{max}}={mathrm{max}}_{i}{X}_{i}$} is ‘atypically larger’ than expected? The cases of
exponential and Gaussian distributed variables are worked out in detail, and the right rate function
for a general pdf in the Gumbel basin of attraction is derived. The…