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Approximate Entropy and Sample Entropy: A Comprehensive Tutorial

NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
Universities Space Research Association, Columbia, MD 21046, USA
Author to whom correspondence should be addressed.
Entropy 2019, 21(6), 541;
Received: 10 May 2019 / Revised: 24 May 2019 / Accepted: 27 May 2019 / Published: 28 May 2019
(This article belongs to the Special Issue Approximate, Sample and Multiscale Entropy)
PDF [797 KB, uploaded 10 June 2019]


Approximate Entropy and Sample Entropy are two algorithms for determining the regularity of series of data based on the existence of patterns. Despite their similarities, the theoretical ideas behind those techniques are different but usually ignored. This paper aims to be a complete guideline of the theory and application of the algorithms, intended to explain their characteristics in detail to researchers from different fields. While initially developed for physiological applications, both algorithms have been used in other fields such as medicine, telecommunications, economics or Earth sciences. In this paper, we explain the theoretical aspects involving Information Theory and Chaos Theory, provide simple source codes for their computation, and illustrate the techniques with a step by step example of how to use the algorithms properly. This paper is not intended to be an exhaustive review of all previous applications of the algorithms but rather a comprehensive tutorial where no previous knowledge is required to understand the methodology.
Keywords: approximate entropy; sample entropy; information theory; chaos theory approximate entropy; sample entropy; information theory; chaos theory
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Delgado-Bonal, A.; Marshak, A. Approximate Entropy and Sample Entropy: A Comprehensive Tutorial. Entropy 2019, 21, 541.

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