Authors: Bajić, Dragana
Mišić, Nataša
Škorić, Tamara
Japundžić-Žigon, Nina
Milovanović, Miloš 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On entropy of probability integral transformed time series
Journal: Entropy
Volume: 22
Issue: 10
First page: Article no. 1146
Issue Date: 1-Oct-2020
Rank: M22
ISSN: 1099-4300
DOI: 10.3390/e22101146
Abstract: 
The goal of this paper is to investigate the changes of entropy estimates when the amplitude distribution of the time series is equalized using the probability integral transformation. The data we analyzed were with known properties—pseudo-random signals with known distributions, mutually coupled using statistical or deterministic methods that include generators of statistically dependent distributions, linear and non-linear transforms, and deterministic chaos. The signal pairs were coupled using a correlation coefficient ranging from zero to one. The dependence of the signal samples is achieved by moving average filter and non-linear equations. The applied coupling methods are checked using statistical tests for correlation. The changes in signal regularity are checked by a multifractal spectrum. The probability integral transformation is then applied to cardiovascular time series—systolic blood pressure and pulse interval—acquired from the laboratory animals and represented the results of entropy estimations. We derived an expression for the reference value of entropy in the probability integral transformed signals. We also experimentally evaluated the reliability of entropy estimates concerning the matching probabilities.
Keywords: Approximate and sample entropy | Copulas | Cross-entropy | Dependency structures | Probability integral transformation
Publisher: MDPI

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