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Open AccessArticle

Theoretical Aspects on Measures of Directed Information with Simulations

Department of Statistics and Actuarial-Financial Mathematics, Lab of Statistics and Data Analysis, University of the Aegean, 83200 Karlovasi, Greece
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These authors contributed equally to this work.
Mathematics 2020, 8(4), 587; https://doi.org/10.3390/math8040587
Received: 21 March 2020 / Revised: 8 April 2020 / Accepted: 10 April 2020 / Published: 15 April 2020
(This article belongs to the Special Issue Probability, Statistics and Their Applications)
Measures of directed information are obtained through classical measures of information by taking into account specific qualitative characteristics of each event. These measures are classified into two main categories, the entropic and the divergence measures. Many times in statistics we wish to emphasize not only on the quantitative characteristics but also on the qualitative ones. For example, in financial risk analysis it is common to take under consideration the existence of fat tails in the distribution of returns of an asset (especially the left tail) and in biostatistics to use robust statistical methods to trim extreme values. Motivated by these needs in this work we present, study and provide simulations for measures of directed information. These measures quantify the information with emphasis on specific parts (or events) of their probability distribution, without losing the whole information of the less significant parts and at the same time by concentrating on the information of the parts we care about the most. View Full-Text
Keywords: information; entropy; divergence; directed information; weighted entropy; weighted divergence information; entropy; divergence; directed information; weighted entropy; weighted divergence
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Gkelsinis, T.; Karagrigoriou, A. Theoretical Aspects on Measures of Directed Information with Simulations. Mathematics 2020, 8, 587.

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