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The RONO (Rank-Order-Normalization) Procedure for Power-Spectrum Analysis of Datasets with Non-Normal Distributions

1
Center for Space Science and Astrophysics and Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, Stanford, CA 94305-4060, USA
2
Research Office for Complex Physical and Biological Systems, 8006 Zurich, Switzerland
3
Biomedical Optics Research Laboratory, Department of Neonatology, University Hospital Zurich, University of Zurich, 8091 Zurich, Switzerland
*
Author to whom correspondence should be addressed.
Algorithms 2020, 13(7), 157; https://doi.org/10.3390/a13070157
Received: 3 June 2020 / Revised: 22 June 2020 / Accepted: 27 June 2020 / Published: 30 June 2020
Standard (Lomb-Scargle, likelihood, etc.) procedures for power-spectrum analysis provide convenient estimates of the significance of any peak in a power spectrum, based—typically—on the assumption that the measurements being analyzed have a normal (i.e., Gaussian) distribution. However, the measurement sequence provided by a real experiment or a real observational program may not meet this requirement. The RONO (rank-order normalization) procedure generates a proxy distribution that retains the rank-order of the original measurements but has a strictly normal distribution. The proxy distribution may then be analyzed by standard power-spectrum analysis. We show by an example that the resulting power spectrum may prove to be quite close to the power spectrum obtained from the original data by a standard procedure, even if the distribution of the original measurements is far from normal. Such a comparison would tend to validate the original analysis. View Full-Text
Keywords: rank-order normalization; spectral analysis rank-order normalization; spectral analysis
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Sturrock, P.; Scholkmann, F. The RONO (Rank-Order-Normalization) Procedure for Power-Spectrum Analysis of Datasets with Non-Normal Distributions. Algorithms 2020, 13, 157.

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