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

Center for Space Science and Astrophysics and Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, Stanford, CA 94305-4060, USA
Research Office for Complex Physical and Biological Systems, 8006 Zurich, Switzerland
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;
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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