Volume 2,  Issue 2, 2001

Article 25

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


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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Improved Inclusion-Exclusion Inequalities for Simplex and Orthant Arrangements
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Refinements of Carleman's Inequality
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Inequalities related to the Chebychev Functional Involving Integrals Over Different Intervals
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Some Distortion Inequalities Associated with the Fractional Derivatives of Analytic and Univalent Functions
H.M. Srivastava, Yi Ling and Gejun Bao

Necessary and Sufficient Condition for Existence and Uniqueness of the Solution of Cauchy Problem for Holomorphic Fuchsian Operators
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Bounds for Entropy and Divergence for Distributions over a Two-Element Set
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