On the characteristic function of the generalized normal distribution

Tibor K. Pogány; Saralees Nadarajah

doi:10.1016/j.crma.2009.12.010

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On the characteristic function of the generalized normal distribution
[Sur la fonction caractéristique de la distribution normale généralisée]

Présenté par : Paul Malliavin

Tibor K. Pogány ¹ ; Saralees Nadarajah ²

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, Volume 348 (2010) no. 3-4, pp. 203-206.

Résumé
Abstract

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 ${}_{1}{Ψ_{0}}$ , la seconde est exprimée via la fonction hypergéométrique gaussienne ${}_{2}{F_{1}}$ .

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 ${}_{1}{Ψ_{0}}$ -function, while the latter is expressed via the Gaussian hypergeometric ${}_{2}{F_{1}}$ .

Reçu le : 2009-11-24
Accepté le : 2009-12-08
Publié le : 2009-12-30

DOI : 10.1016/j.crma.2009.12.010

Affiliations des auteurs :

Tibor K. Pogány ¹ ; Saralees Nadarajah 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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     author = {Tibor K. Pog\'any and Saralees Nadarajah},
     title = {On the characteristic function of the generalized normal distribution},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {203--206},
     publisher = {Elsevier},
     volume = {348},
     number = {3-4},
     year = {2010},
     doi = {10.1016/j.crma.2009.12.010},
     language = {en},
}

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Tibor K. Pogány; Saralees Nadarajah. On the characteristic function of the generalized normal distribution. Comptes Rendus. Mathématique, Volume 348 (2010) no. 3-4, pp. 203-206. doi : 10.1016/j.crma.2009.12.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.12.010/

Bibliographie
Cité par

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