Renyi entropy in continuous case is not the limit of discrete case

Year 2016, Volume: 4 Issue: 1, 113 - 117, 15.04.2016

M. Sanei Tabass G. R. Mohtashami Borzadaran M. Amini

https://doi.org/10.36753/mathenot.421418

Cited By: 7

Abstract

Shannon entropy is the creation of Shannon (1948) based on the experiences in Bell System Company
during and after the Second World War. Then, Renyi (1961) generalized it for one parameter families of
entropies. This entropy for discrete random variables is non-negative but it can be negative in continuous
case.
In this paper, we show that Renyi entropy for continuous random variables is not equal to the limit of it
for discrete random variables. Also, some notes are derived in view of the variate versions of entropy
criteria. 

Keywords

Vector valued Dirichlet series (VVDS), relative Ritt order, relative Ritt lower order, growth

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