Geodesic
On the properties of the Generalized Normal Distribution
Discussiones Mathematicae. Probability and Statistics, Tome 34 (2014) no. 1-2, pp. 35-49

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The target of this paper is to provide a critical review and to enlarge the theory related to the Generalized Normal Distributions (GND). This three term (position, scale shape) distribution is based in a strong theoretical background due to Logarithm Sobolev Inequalities. Moreover, the GND is the appropriate one to support the Generalized entropy type Fisher's information measure.
Keywords: entropy type Fisher's information, Shannon entropy, Normal distribution, truncated distribution 
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Toulias, Thomas; Kitsos, Christos. On the properties of the Generalized Normal Distribution. Discussiones Mathematicae. Probability and Statistics, Tome 34 (2014) no. 1-2, pp. 35-49. http://geodesic.mathdoc.fr/item/DMPS_2014_34_1-2_a2/