Inequalities for the Fisher’s Information Measures

Christos P. Kitsos () and Thomas L. Toulias ()
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Christos P. Kitsos: Technological Educational Institute of Athens
Thomas L. Toulias: Technological Educational Institute of Athens

A chapter in Handbook of Functional Equations, 2014, pp 281-313 from Springer

Abstract: Abstract The objective of this chapter is to provide a thorough discussion on inequalities related to the entropy measures in connection to the γ-order generalized normal distribution (γ–GND). This three-term (position, scale and shape) family of distributions plays the role of the usual multivariate normal distribution in information theory. Moreover, the γ–GND is the appropriate family of distributions to support a generalized version of the entropy type Fisher’s information measure. This generalized (entropy type) Fisher’s information is also discussed as well as the generalized entropy power, while the γ-GND heavily contributes to these generalizations. The appropriate bounds and inequalities of these measures are also provided.

Keywords: Fisher’s entropy type information measure; Shannon entropy; Generalized normal distribution (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4939-1246-9_13

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DOI: 10.1007/978-1-4939-1246-9_13

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