Inequalities for the Fisher's Information Measures

• Published in: Handbook of Functional Equations Vol. 95; pp. 281 - 313
• Main Authors: Kitsos, Christos P., Toulias, Thomas L.
• Format: Book Chapter
• Language: English
• Published: United States Springer 01.01.2014; Springer New York
• Series: Springer Optimization and Its Applications
• Subjects: Differential equations; Fisher’s entropy type information measure; Generalized normal distribution; Maths for engineers; Optimization; Shannon entropy
• ISBN: 9781493912452; 1493912453
• ISSN: 1931-6828; 1931-6836
• DOI: 10.1007/978-1-4939-1246-9_13

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.