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Entropy 2014, 16(3), 1743-1755; doi:10.3390/e16031743
Article

Transfer Entropy Expressions for a Class of Non-Gaussian Distributions

1,2,*  and 1
1 Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden 2 Center for Biosciences, Department of Biosciences and Nutrition, Karolinska Institutet, SE-141 83 Huddinge, Sweden
* Author to whom correspondence should be addressed.
Received: 17 January 2014 / Revised: 10 March 2014 / Accepted: 18 March 2014 / Published: 24 March 2014
(This article belongs to the Special Issue Transfer Entropy)
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Abstract

Transfer entropy is a frequently employed measure of conditional co-dependence in non-parametric analysis of Granger causality. In this paper, we derive analytical expressions for transfer entropy for the multivariate exponential, logistic, Pareto (type IIV) and Burr distributions. The latter two fall into the class of fat-tailed distributions with power law properties, used frequently in biological, physical and actuarial sciences. We discover that the transfer entropy expressions for all four distributions are identical and depend merely on the multivariate distribution parameter and the number of distribution dimensions. Moreover, we find that in all four cases the transfer entropies are given by the same decreasing function of distribution dimensionality.
Keywords: Granger causality; information theory; transfer entropy; multivariate distributions; power-law distributions Granger causality; information theory; transfer entropy; multivariate distributions; power-law distributions
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.

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Jafari-Mamaghani, M.; Tyrcha, J. Transfer Entropy Expressions for a Class of Non-Gaussian Distributions. Entropy 2014, 16, 1743-1755.

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