Renyi entropy in continuous case is not the limit of discrete case
Copyright policy )Renyi entropy in continuous case is not the limit of discrete case
Summary: Shannon entropy is the creation by \textit{C. E. Shannon} [Bell Syst. Tech. J. 27, 379--423, 623--656 (1948; Zbl 1154.94303)] based on the experiences in Bell System Company during and after the Second World War. Then, \textit{A. Rényi} [in: Proc. 4th Berkeley Symp. Math. Stat. Probab. 1. Berkeley, CA: University of California Press. 547--561 (1961; Zbl 0106.33001)] 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.
Renyi entropy, Characterization and structure theory of statistical distributions, Riemann integrable, continuous random variable, Shannon entropy, Statistical aspects of information-theoretic topics, Vector valued Dirichlet series (VVDS);relative Ritt order;relative Ritt lower order;growth, information theory
Renyi entropy, Characterization and structure theory of statistical distributions, Riemann integrable, continuous random variable, Shannon entropy, Statistical aspects of information-theoretic topics, Vector valued Dirichlet series (VVDS);relative Ritt order;relative Ritt lower order;growth, information theory
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