An Open-Source Toolkit For Entropic Time Series Analysis

EntropyHub.jl is part of the EntropyHub project.

For more info visit:

Also available with: Matlab // Python

Latest Updates


––- New multivariate methods ––-

Five new multivariate entropy functions incorporating several method-specific variations

––- New multivariate multiscale methods ––-

Two new multivariate multiscale entropy functions

––- Extra signal processing tools ––-

WindowData() is a new function that allows users to segment data (univariate or multivariate time series) into windows with/without overlapping samples! This allows users to calculate entropy on subsequences of their data to perform analyses with greater time resolution.

Other little fixes...

––- Docs edits ––-

  • Examples in the documentation were updated to match the latest package syntax.


This toolkit provides a wide range of functions to calculate different entropy statistics. There is an ever-growing range of information-theoretic and dynamical systems entropy measures presented in the scientific literature. The goal of EntropyHub.jl is to integrate the many established entropy methods in one open-source package with an extensive documentation and consistent syntax [that is also accessible in multiple programming languages (Matlab, Python)].


Information and uncertainty can be regarded as two sides of the same coin: the more uncertainty there is, the more information we gain by removing that uncertainty. In the context of information and probability theory, Entropy quantifies that uncertainty.

Various measures have been derived to estimate entropy (uncertainty) from discrete time series, each seeking to best capture the uncertainty of the system under examination. This has resulted in many entropy statistics from approximate entropy and sample entropy, to multiscale sample entropy and refined-composite multiscale cross-sample entropy.

The goal of EntropyHub is to provide a comprehensive set of functions with a simple and consistent syntax that allows the user to augment parameters at the command line, enabling a range from basic to advanced entropy methods to be implemented with ease.


It is important to clarify that the entropy functions herein described estimate entropy in the context of probability theory and information theory as defined by Shannon, and not thermodynamic or other entropies from classical physics.


Using the Julia REPL:

julia> using Pkg; Pkg.add("EntropyHub")


julia> ] 
pkg> add EntropyHub

To get the latest version of EntropyHub directly from GitHub:

julia> ] 
pkg> add


EntropyHub is licensed under the Apache License (Version 2.0) and is free to use by all on condition that the following reference be included on any outputs realized using the software:

Matthew W. Flood (2021),
EntropyHub: An Open-Source Toolkit for Entropic Time Series Analysis,
PLoS ONE 16(11):e0259448
DOI:  10.1371/journal.pone.0259448 

    © Copyright 2024 Matthew W. Flood, EntropyHub
    Licensed under the Apache License, Version 2.0 (the "License");
    you may not use this file except in compliance with the License.
    You may obtain a copy of the License at
    Unless required by applicable law or agreed to in writing, software
    distributed under the License is distributed on an "AS IS" BASIS,
    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    See the License for the specific language governing permissions and
    limitations under the License.
    For Terms of Use see

If you find this package useful, please consider starring it on GitHub and Julia Packages (or MatLab File Exchange and PyPI). This helps us to gauge user satisfaction.


For general queries and information about EntropyHub, contact:

If you have any questions or need help using the package, please contact us at:

If you notice or identify any issues, please do not hesitate to contact us at:

We will do our best to help you with any relevant issues that you may have.

If you come across any errors or technical issues, you can raise these under the issues tab on the EntropyHub.jl GitHub page. Similarly, if you have any suggestions or recommendations on how this package can be improved, please let us know.

Thank you for using EntropyHub,


Function List

EntropyHub functions fall into 8 categories:

  • Base functions for estimating the entropy of a single univariate time series.
  • Cross functions for estimating the entropy between two univariate time series.
  • Bidimensional functions for estimating the entropy of a two-dimensional univariate matrix.
  • Multiscale functions for estimating the multiscale entropy of a single univariate time series using any of the Base entropy functions.
  • Multiscale Cross functions for estimating the multiscale entropy between two univariate time series using any of the Cross-entropy functions.
  • Multivariate Multiscale functions for estimating the multivariate multiscale entropy of multivariate dataset using any of the Multivariate-entropy functions.
  • Other Supplementary functions for various tasks related to EntropyHub and signal processing.
     ___  _   _  _____  _____  ____  ____  _     _          
    |  _|| \ | ||_   _||     \|    ||    || \   / |   ___________ 
    | \_ |  \| |  | |  |   __/|    ||  __| \ \_/ /   /  _______  \
    |  _|| \ \ |  | |  |   \  |    || |     \   /   |  /  ___  \  |
    | \_ | |\  |  | |  | |\ \ |    || |      | |    | |  /   \  | | 
    |___||_| \_|  |_|  |_| \_||____||_|      |_|   _|_|__\___/  | | 
     _   _  _   _  ____                           / |__\______\/  | 
    | | | || | | ||    \     An open-source      |  /\______\__|_/ 
    | |_| || | | ||    |     toolkit for         | |  /   \  | | 
    |  _  || | | ||    \     entropic time-      | |  \___/  | |          
    | | | || |_| ||     \    series analysis     |  \_______/  |
    |_| |_|\_____/|_____/                         \___________/

Documentation for EntropyHub.