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

Sturrock, Peter; Scholkmann, Felix (2020). The RONO (Rank-Order-Normalization) Procedure for Power-Spectrum Analysis of Datasets with Non-Normal Distributions. Algorithms, 13(7):157.

## Abstract

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.

## Abstract

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.

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