Volume 2,
Issue 2, 2001
Article
25
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BOUNDS FOR ENTROPY AND DIVERGENCE FOR DISTRIBUTIONS OVER A TWO-ELEMENT SET
FLEMMING
TOPSOE
DEPARTMENT OF MATHEMATICS
UNIVERSITY OF COPENHAGEN
UNIVERSITETSPARKEN 5
DK-2100 COPENHAGEN, DENMARK.
E-Mail: topsoe@math.ku.dk
Received 6 November, 2000; accepted 6 March, 2001.
Communicated by: F. Hansen
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ABSTRACT.
Three results dealing with probability distributions (p,q) over a
two-element set are presented. The two first give bounds for the entropy
function H(p,q) and are referred to as the logarithmic and the
power-type bounds, respectively. The last result is a refinement of
well known Pinsker-type inequalities for information divergence.
The refinement readily extends to general distributions,
but the key case to consider involves distributions on a two-element set.
The discussion points to some elementary, yet non-trivial
problems concerning seemingly simple concrete functions.
Key words:
Entropy, divergence,
Pinsker's inequality.
2000 Mathematics Subject
Classification:
94A17, 26D15.
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