{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T17:09:00Z","timestamp":1775754540039,"version":"3.50.1"},"reference-count":43,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2018,12,13]],"date-time":"2018-12-13T00:00:00Z","timestamp":1544659200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000925","name":"National Health and Medical Research Council","doi-asserted-by":"publisher","award":["1091593"],"award-info":[{"award-number":["1091593"]}],"id":[{"id":"10.13039\/501100000925","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000925","name":"National Health and Medical Research Council","doi-asserted-by":"publisher","award":["1060312"],"award-info":[{"award-number":["1060312"]}],"id":[{"id":"10.13039\/501100000925","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Approximate entropy (ApEn) and sample entropy (SampEn) are widely used for temporal complexity analysis of real-world phenomena. However, their relationship with the Hurst exponent as a measure of self-similarity is not widely studied. Additionally, ApEn and SampEn are susceptible to signal amplitude changes. A common practice for addressing this issue is to correct their input signal amplitude by its standard deviation. In this study, we first show, using simulations, that ApEn and SampEn are related to the Hurst exponent in their tolerance r and embedding dimension m parameters. We then propose a modification to ApEn and SampEn called range entropy or RangeEn. We show that RangeEn is more robust to nonstationary signal changes, and it has a more linear relationship with the Hurst exponent, compared to ApEn and SampEn. RangeEn is bounded in the tolerance r-plane between 0 (maximum entropy) and 1 (minimum entropy) and it has no need for signal amplitude correction. Finally, we demonstrate the clinical usefulness of signal entropy measures for characterisation of epileptic EEG data as a real-world example.<\/jats:p>","DOI":"10.3390\/e20120962","type":"journal-article","created":{"date-parts":[[2018,12,14]],"date-time":"2018-12-14T03:58:17Z","timestamp":1544759897000},"page":"962","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":64,"title":["Range Entropy: A Bridge between Signal Complexity and Self-Similarity"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4744-8721","authenticated-orcid":false,"given":"Amir","family":"Omidvarnia","sequence":"first","affiliation":[{"name":"The Florey Institute of Neuroscience and Mental Health, Austin Campus, Heidelberg, VIC 3084, Australia"},{"name":"Faculty of Medicine, Dentistry and Health Sciences, The University of Melbourne, VIC 3010, Australia"}]},{"given":"Mostefa","family":"Mesbah","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Sultan Qaboos University, Muscat 123, Oman"}]},{"given":"Mangor","family":"Pedersen","sequence":"additional","affiliation":[{"name":"The Florey Institute of Neuroscience and Mental Health, Austin Campus, Heidelberg, VIC 3084, Australia"}]},{"given":"Graeme","family":"Jackson","sequence":"additional","affiliation":[{"name":"The Florey Institute of Neuroscience and Mental Health, Austin Campus, Heidelberg, VIC 3084, Australia"},{"name":"Faculty of Medicine, Dentistry and Health Sciences, The University of Melbourne, VIC 3010, Australia"},{"name":"Department of Neurology, Austin Health, Melbourne, VIC 3084, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"560","DOI":"10.3390\/e17020560","article-title":"Symbolic Entropy of the Amplitude rather than the Instantaneous Frequency of EEG Varies in Dementia","volume":"17","author":"Lin","year":"2015","journal-title":"Entropy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"6573","DOI":"10.3390\/e16126573","article-title":"Automatic Sleep Stages Classification Using EEG Entropy Features and Unsupervised Pattern Analysis Techniques","volume":"16","author":"Peluffo","year":"2014","journal-title":"Entropy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"231","DOI":"10.3390\/e17010231","article-title":"Multiscale Entropy Analysis of Heart Rate Variability for Assessing the Severity of Sleep Disordered Breathing","volume":"17","author":"Pan","year":"2015","journal-title":"Entropy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"e4817","DOI":"10.7717\/peerj.4817","article-title":"Sample entropy analysis for the estimating depth of anaesthesia through human EEG signal at different levels of unconsciousness during surgeries","volume":"6","author":"Liu","year":"2018","journal-title":"PeerJ"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1320","DOI":"10.7150\/ijbs.19462","article-title":"Complexity Change in Cardiovascular Disease","volume":"13","author":"Chen","year":"2017","journal-title":"Int. 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