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Recently, it has been conjectured that the statistics of extremes is ofrelevance for a large class of correlated system. For certain probabilitydensities 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 thethree-dimensional Edward-Anderson Ising spin glass at and below the criticaltemperature, even where $P(q)$ is exponentially small. We find that aprobability distribution related to extreme order statistics gives an excellentdescription of $P(q)$ over about 80 orders of magnitude.Comment: 4 pages RevTex, 3 figure

Functional form of the Parisi overlap distribution for the three-dimensional Edwards-Anderson Ising spin glass