- Mathematical Sciences and Applications E-Notes
- Vol: 4 Issue: 1
- Renyi entropy in continuous case is not the limit of discrete case
Renyi entropy in continuous case is not the limit of discrete case
Authors : M. Sanei Tabass, G. R. Mohtashami Borzadaran, M. Amini
Pages : 113-117
Doi:10.36753/mathenot.421418
View : 7 | Download : 6
Publication Date : 2016-04-15
Article Type : Research
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