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On the convexity of higher order Jensen differences based on entropy functions (Corresp.)

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2 Author(s)

In an earlier work, the authors introduced a divergence measure, called the first-order Jensen difference, or in shortcal j-divergence, which is based on entropy functions of degreealpha. This provided a generalization of the measure of mutual information based on Shannon's entropy (corresponding toalpha = 1). It was shown that the first-ordercal j-divergence is a convex function only when a is restricted to some range. We define higher order Jensen differences and show that they are convex functions only when the underlying entropy function is of degree two. A statistical application requiring the convexity of higher order Jensen differences is indicated.

Published in:

Information Theory, IEEE Transactions on  (Volume:28 ,  Issue: 6 )

Date of Publication:

Nov 1982

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