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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.
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