no. 3-4
Statistics
On the characteristic function of the generalized normal distribution
[Sur la fonction caractéristique de la distribution normale généralisée]

Présenté par : Paul Malliavin

Pogány, Tibor K.1 ; Nadarajah, Saralees2
1 Faculty of Maritime Studies, University of Rijeka, 51000 Rijeka, Croatia
2 School of Mathematics, University of Manchester, Manchester M13 9PL, UK
Comptes Rendus. Mathématique, Tome 348 (2010) no. 3-4, pp. 203-206.

Pour la première fois on déduit une expression explicite de la fonction caractéristique de la distribution normale généralisée (GND). On déduit aussi une expression du coefficient de corrélation entre les valeurs d'une variable et leurs rangs dans les échantillonnages de la distribution normale généralisée. La première expression utilise la fonction hypergéométrique confluente de Fox–Wright Ψ01, la seconde est exprimée via la fonction hypergéométrique gaussienne F12.

For the first time, an explicit closed form expression is derived for the characteristic function of the generalized normal distribution (GND). Also derived is an expression for the correlation coefficient between variate-values and their ranks in samples from the GND. The expression for the former involves the Fox–Wright generalized confluent hypergeometric Ψ01-function, while the latter is expressed via the Gaussian hypergeometric F12.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.12.010
Pogány, Tibor K. 1 ; Nadarajah, Saralees 2

1 Faculty of Maritime Studies, University of Rijeka, 51000 Rijeka, Croatia
2 School of Mathematics, University of Manchester, Manchester M13 9PL, UK 
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Pogány, Tibor K.; Nadarajah, Saralees. On the characteristic function of the generalized normal distribution. Comptes Rendus. Mathématique, Tome 348 (2010) no. 3-4, pp. 203-206. doi : 10.1016/j.crma.2009.12.010. http://www.numdam.org/articles/10.1016/j.crma.2009.12.010/

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