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January 2021 Stein's method in two limit theorems involving the generalized inverse Gaussian distribution
Essomanda KONZOU, Efoévi KOUDOU, Kossi Essona GNEYOU
Afr. Stat. 16(1): 2561-2586 (January 2021). DOI: 10.16929/as/2021.2559.174


The generalized hyperbolic (GH) distribution converges in law to the generalized inverse Gaussian (GIG) distribution under certain conditions on the parameters. When the edges of an infinite rooted tree are equipped with independent resistances that are inverse Gaussian or reciprocal inverse Gaussian distributions, the total resistance converges almost surely to some random variable which follows the reciprocal inverse Gaussian (RIG) distribution. In this paper we provide explicit upper bounds for the distributional distance between GH (resp. infinite tree) distribution and their limiting GIG (resp. RIG) distribution applying Stein's method.

Sous certaines conditions sur ses paramètres, la loi hyperbolique généralisée (GH) converge vers la loi gaussienne inverse généralisée (GIG). Lorsque les arêtes d'un arbre infini sont munies de résistances aléatoires indépendantes, de loi gaussienne inverse ou de loi gaussienne inverse réciproque, la résistance équivalente converge presque sûrement vers une variable aléatoire de loi gaussienne inverse réciproque (RIG). Dans cet article, nous déterminons des majorants explicites de la distance probabiliste entre la loi GH (resp. un circuit arborescent) et la loi limite GIG (resp. RIG) en appliquant la méthode de Stein.


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Essomanda KONZOU. Efoévi KOUDOU. Kossi Essona GNEYOU. "Stein's method in two limit theorems involving the generalized inverse Gaussian distribution." Afr. Stat. 16 (1) 2561 - 2586, January 2021.


Published: January 2021
First available in Project Euclid: 11 July 2021

Digital Object Identifier: 10.16929/as/2021.2559.174

Primary: 41A25
Secondary: 60E05 , 60F05

Keywords: generalized hyperbolic distribution , generalized inverse Gaussian distribution , reciprocal inverse Gaussian distribution , Stein characterization , Stein equation , Taylor expansion

Rights: Copyright © 2021 The Statistics and Probability African Society


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Vol.16 • No. 1 • January 2021
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