The analysis of indexed astronomical time series – XI. The statistics of oversampled white noise periodograms
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Date
2015
Authors
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Journal ISSN
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Publisher
Oxford University Press
Abstract
The distribution of the maxima of periodograms is considered in the case where the time
series is made up of regularly sampled, uncorrelated Gaussians. It is pointed out that if there
is no oversampling, then for large data sets, the known distribution of maxima tends to a oneparameter
Gumbel distribution. Simulations are used to demonstrate that for oversampling by
large factors, a two-parameter Gumbel distribution provides a highly accurate representation
of the simulation results. As the oversampling approaches the continuous limit, the twoparameter
Gumbel distribution takes on a simple form which depends only on the logarithm
of the number of data. Subsidiary results are the autocorrelation function of the oversampled
periodogram; expressions for the accuracy of simulated percentiles; and the relation between
percentiles of the periodogram and the amplitude spectrum.
Description
Keywords
Astronomy, Gaussians, Gumbel distribution, Periodograms, Statistics, Large data sets
Citation
Koen, C. (2015). The analysis of indexed astronomical time series – XI. The statistics of oversampled white noise periodograms. Monthly Notices of the Royal Astronomical Society, 449(1): 1098-1105.