  The least-squares (or Lomb-Scargle) periodogram is a powerful tool which is
used routinely in many branches of astronomy to search for periodicities in
observational data. The problem of assessing statistical significance of
candidate periodicities for different periodograms is considered. Based on
results in extreme value theory, improved analytic estimations of false alarm
probabilities are given. They include an upper limit to the false alarm
probability (or a lower limit to the significance). These estimations are
tested numerically in order to establish regions of their practical
applicability.
