  Recently, it has been conjectured that the statistics of extremes is of
relevance for a large class of correlated system. For certain probability
densities this predicts the characteristic large $x$ fall-off behavior
$f(x)\sim\exp (-a e^x)$, $a>0$. Using a multicanonical Monte Carlo technique,
we have calculated the Parisi overlap distribution $P(q)$ for the
three-dimensional Edward-Anderson Ising spin glass at and below the critical
temperature, even where $P(q)$ is exponentially small. We find that a
probability distribution related to extreme order statistics gives an excellent
description of $P(q)$ over about 80 orders of magnitude.
