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.
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Kitsos, C., Toulias, T. (2014). Inequalities for the Fisher’s Information Measures. In: Rassias, T. (eds) Handbook of Functional Equations. Springer Optimization and Its Applications, vol 95. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1246-9_13
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