Abstract
We derive the representation of generalized additive measures of information, depending on two probability distributions and having the sum property with a regular generating function. This family of measures includes the Shannon entropy, the entropy of degree (α,β), the generalized information energy, the sine entropy and the generalized directed divergence.
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Sander, W. On a functional equation arising in information theory. Manuscripta Math 54, 439–452 (1986). https://doi.org/10.1007/BF01168486
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DOI: https://doi.org/10.1007/BF01168486