It is often necessary to determine the probability that the peaks in a time history will exceed certain values. This is done using a peak probability distribution which only considers the peaks in the time history and not values at any arbitrary time.
For a narrow banded process which has a Gaussian probability distribution, the peaks follow a Rayleigh probability distribution.
An example is the variation of wave height in a sea where swell is the main component.
Sky wave field intensities follow the Rayleigh distribution for one minute or smaller time intervals.