Some properties of generalized exponential entropies with applications to data compression

• I. Csiszár discussed generalized entropies in his lecture at the Sixth Prague Conference on Information Theory. The authors emphasize that Csiszár noted the link between certain lower bounds for the quantization error and Rényi's differential entropy of order $\alpha$. Another important reference is the paper by L. L. Campbell where the concept of an exponential entropy was introduced. The authors investigate "several consequences that are of interest in the theory of data (or signal) compression". They also "investigate especially the exponential families of distributions, in particular the Miller-Thomas (or generalized Gaussian) family of distributions". The paper is a detailed discussion of the aforementioned problems coupled with examples and details of the possible applications. Exponential entropy is calculated for the uniform distribution, the univariate Gaussian distribution, the Laplace distribution, the Miller-Thomas distribution, an infinite-dimensional Gaussian exponential family, the Gauss-Laplace mixture and the multivariate Gaussian distribution. The extent of a distribution is given for the shape parameter in the Miller-Thomas distribution. Campbell's representation for E$[\alpha, 1 ; f]$ and the connection between an entropy series and data compression are discussed. A lower bound for the entropy of a partition (as defined in the paper) is given. Examples and proofs are illustrated with outputs from Mathematica.

Ämnesord

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

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Matematik

Mathematics

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