  I propose a new procedure to estimate the False Alarm Probability, the
measure of significance for peaks of periodograms. The key element of the new
procedure is the use of generalized extreme-value distributions, the limiting
distribution for maxima of variables from most continuous distributions. This
technique allows reliable extrapolation to the very high probability levels
required by multiple hypothesis testing, and enables the derivation of
confidence intervals of the estimated levels. The estimates are stable against
deviations from distributional assumptions, which are otherwise usually made
either about the observations themselves or about the theoretical univariate
distribution of the periodogram. The quality and the performance of the
procedure is demonstrated on simulations and on two multimode variable stars
from Sloan Digital Sky Survey Stripe 82.
