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Inequalities for the Fisher’s Information Measures

In: Handbook of Functional Equations

Author

Listed:
  • Christos P. Kitsos

    (Technological Educational Institute of Athens)

  • Thomas L. Toulias

    (Technological Educational Institute of Athens)

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.

Suggested Citation

  • Christos P. Kitsos & Thomas L. Toulias, 2014. "Inequalities for the Fisher’s Information Measures," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Handbook of Functional Equations, edition 127, pages 281-313, Springer.
    • Handle: RePEc:spr:spochp:978-1-4939-1246-9_13
    DOI: 10.1007/978-1-4939-1246-9_13
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