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Rényi entropy

In information theory, Rényi entropy, an extension of Shannon entropy, is a means of quantifying the entropy of a system. Entropy characterizes the disorder of the system, how much information can be compressed and consequently how much information is present in a signal or system (see Information entropy). Rényi entropy is defined as

H_\alpha(p_1,p_2,\ldots,p_n) = \frac{1}{1-\alpha}\ln\Bigg(\sum_{i=1}^n p_i^\alpha\Bigg)

where pi are probabilities and \alpha > 0, \alpha \ne 1. As α approaches 1, Hα converges to Shannon entropy. For some α and α' where \alpha \le \alpha', Rényi entropy guarantees that

H_\alpha \le H_{\alpha'}.
01-04-2007 01:16:19
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