Shannon type inequalities via time scales theory

The aim of present paper is to obtain Shannon type inequalities using the extended version of Jensen’s inequality in time scales settings. The concept of differential entropy of a continuous random variable on time scales is introduced, and its bounds for some particular distributions are also estim...

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Bibliographic Details
Published in:Advances in difference equations 2020-03, Vol.2020 (1), p.1-14, Article 135
Main Authors: Ansari, Iqrar, Khan, Khuram Ali, Nosheen, Ammara, Pečarić, Ðilda, Pečarić, Josip
Format: Article
Language:English
Subjects:
Analysis
Continuity (mathematics)
Convex function
Difference and Functional Equations
Functional Analysis
Inequalities
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Random variables
Shannon entropy
Time
Time scale calculus
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Summary:The aim of present paper is to obtain Shannon type inequalities using the extended version of Jensen’s inequality in time scales settings. The concept of differential entropy of a continuous random variable on time scales is introduced, and its bounds for some particular distributions are also estimated.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-020-02587-z