Comptes Rendus
Statistics
On the characteristic function of the generalized normal distribution
[Sur la fonction caractéristique de la distribution normale généralisée]
Comptes Rendus. Mathématique, Volume 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

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
@article{CRMATH_2010__348_3-4_203_0,
     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},
}
TY  - JOUR
AU  - Tibor K. Pogány
AU  - Saralees Nadarajah
TI  - On the characteristic function of the generalized normal distribution
JO  - Comptes Rendus. Mathématique
PY  - 2010
SP  - 203
EP  - 206
VL  - 348
IS  - 3-4
PB  - Elsevier
DO  - 10.1016/j.crma.2009.12.010
LA  - en
ID  - CRMATH_2010__348_3-4_203_0
ER  - 
%0 Journal Article
%A Tibor K. Pogány
%A Saralees Nadarajah
%T On the characteristic function of the generalized normal distribution
%J Comptes Rendus. Mathématique
%D 2010
%P 203-206
%V 348
%N 3-4
%I Elsevier
%R 10.1016/j.crma.2009.12.010
%G en
%F CRMATH_2010__348_3-4_203_0
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/

[1] C. Kleiber; S. Kotz Statistical Size Distributions in Economics and Actuarial Sciences, John Wiley and Sons, Hoboken, NJ, 2003

[2] G. Lunetta Di una generalizzazione dello schema della curva normale, Annali della Facoltà di Economia e Commercio di Palermo, Volume 17 (1963), pp. 237-244

[3] T.A. Maturi; A. Elsayigh The correlation between variate-values and ranks in samples from complete fourth power exponential distribution, Journal of Mathematics Research, Volume 1 (2009), pp. 14-18

[4] S. Nadarajah A generalized normal distribution, Journal of Applied Statistics, Volume 32 (2005), pp. 685-694

[5] T.K. Pogány, Closed expression for characteristic function of CEPE distribution, Journal of Mathematics Research (2009), in press

[6] T.K. Pogány; H.M. Srivastava; Ž. Tomovski Some families of Mathieu a-series and alternating Mathieu a-series, Applied Mathematics and Computation, Volume 173 (2006), pp. 69-108

[7] A. Stuart The correlation between variate-values and ranks in samples from a continuous distribution, British Journal of Statistical Psychology, Volume 7 (1954), pp. 37-44

[8] A. Stuart The correlation between variate-values and ranks in samples from a distributions having no variance, British Journal of Statistical Psychology, Volume 8 (1955), pp. 25-27

[9] M.Th. Subbotin On the law of frequency of error, Matematicheskiĭ Sbornik, Volume 31 (1923), pp. 296-301

Cité par Sources :

Commentaires - Politique