On Entropy of Probability Integral Transformed Time Series
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 us...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-10-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/22/10/1146 |
| _version_ | 1827704509732749312 |
|---|---|
| author | Dragana Bajić Nataša Mišić Tamara Škorić Nina Japundžić-Žigon Miloš Milovanović |
| author_facet | Dragana Bajić Nataša Mišić Tamara Škorić Nina Japundžić-Žigon Miloš Milovanović |
| author_sort | Dragana Bajić |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T15:42:50Z |
| format | Article |
| id | doaj.art-c8ddc8ac544b4ef5aff8ce8a3d4104c8 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T15:42:50Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-c8ddc8ac544b4ef5aff8ce8a3d4104c82023-11-20T16:44:22ZengMDPI AGEntropy1099-43002020-10-012210114610.3390/e22101146On Entropy of Probability Integral Transformed Time SeriesDragana Bajić0Nataša Mišić1Tamara Škorić2Nina Japundžić-Žigon3Miloš Milovanović4Faculty of Technical Sciences, University of Novi Sad, 21000 Novi Sad, SerbiaResearch and Development Institute Lola Ltd., 11000 Belgrade, SerbiaFaculty of Technical Sciences, University of Novi Sad, 21000 Novi Sad, SerbiaFaculty of Medicine, University of Belgrade, 11000 Belgrade, SerbiaMathematical Institute of the Serbian Academy of Sciences and Arts, 11000 Beograd, SerbiaThe 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.https://www.mdpi.com/1099-4300/22/10/1146approximate and sample entropycross-entropycopulasprobability integral transformationdependency structures |
| spellingShingle | Dragana Bajić Nataša Mišić Tamara Škorić Nina Japundžić-Žigon Miloš Milovanović On Entropy of Probability Integral Transformed Time Series Entropy approximate and sample entropy cross-entropy copulas probability integral transformation dependency structures |
| title | On Entropy of Probability Integral Transformed Time Series |
| title_full | On Entropy of Probability Integral Transformed Time Series |
| title_fullStr | On Entropy of Probability Integral Transformed Time Series |
| title_full_unstemmed | On Entropy of Probability Integral Transformed Time Series |
| title_short | On Entropy of Probability Integral Transformed Time Series |
| title_sort | on entropy of probability integral transformed time series |
| topic | approximate and sample entropy cross-entropy copulas probability integral transformation dependency structures |
| url | https://www.mdpi.com/1099-4300/22/10/1146 |
| work_keys_str_mv | AT draganabajic onentropyofprobabilityintegraltransformedtimeseries AT natasamisic onentropyofprobabilityintegraltransformedtimeseries AT tamaraskoric onentropyofprobabilityintegraltransformedtimeseries AT ninajapundziczigon onentropyofprobabilityintegraltransformedtimeseries AT milosmilovanovic onentropyofprobabilityintegraltransformedtimeseries |