On weak law of large numbers for sums of negatively superadditive dependent random variables

Habib Naderi; Przemysław Matuła; Mahdi Salehi; Mohammad Amini

doi:10.5802/crmath.7

Probabilités, Statistiques

On weak law of large numbers for sums of negatively superadditive dependent random variables
[Sur la loi faible des grands nombres pour des sommes pondérées de variables aléatoires négativement superadditivement-dépendantes]

Habib Naderi ¹ ; Przemysław Matuła ² ; Mahdi Salehi ³ ; Mohammad Amini ⁴

¹ Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
² Institute of Mathematics, Marie Curie-Skłodowska University, pl. M.C.-Skłodowskiej 1, 20-031 Lublin, Poland
³ Department of Mathematics and Statistics, University of Neyshabur, Neyshabur, Iran
⁴ Department of Statistics, Ordered data, reliability and dependency Center of Excellence, Ferdowsi University of Mashhad, P.O. Box 91775-1159, Mashhad, Iran

Comptes Rendus. Mathématique, Volume 358 (2020) no. 1, pp. 13-21.

Résumé
Abstract

Dans cet article, nous étendons la loi faible des grands nombres de Kolmogorov–Feller à des sommes pondérées maximales de variables aléatoires négativement superadditivement-dépendantes (NSD). En outre, nous construisons une étude de simulation du comportement asymptotique au sens de la convergence en probabilité pour les sommes pondérées de variables aléatoires NSD.

In this paper, we extend Kolmogorov–Feller weak law of large numbers for maximal weighted sums of negatively superadditive dependent (NSD) random variables. In addition, we make a simulation study for the asymptotic behavior in the sense of convergence in probability for weighted sums of NSD random variables.

Reçu le : 2019-03-20
Révisé le : 2019-10-23
Accepté le : 2020-01-10
Publié le : 2020-03-18

DOI : 10.5802/crmath.7

Classification : 60F05, 60F15, 65C10

Affiliations des auteurs :

Habib Naderi ¹ ; Przemysław Matuła ² ; Mahdi Salehi ³ ; Mohammad Amini ⁴

¹ Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
² Institute of Mathematics, Marie Curie-Skłodowska University, pl. M.C.-Skłodowskiej 1, 20-031 Lublin, Poland
³ Department of Mathematics and Statistics, University of Neyshabur, Neyshabur, Iran
⁴ Department of Statistics, Ordered data, reliability and dependency Center of Excellence, Ferdowsi University of Mashhad, P.O. Box 91775-1159, Mashhad, Iran

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Habib Naderi and Przemys{\l}aw Matu{\l}a and Mahdi Salehi and Mohammad Amini},
     title = {On weak law of large numbers for sums of negatively superadditive dependent random variables},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {13--21},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {1},
     year = {2020},
     doi = {10.5802/crmath.7},
     language = {en},
}

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Habib Naderi; Przemysław Matuła; Mahdi Salehi; Mohammad Amini. On weak law of large numbers for sums of negatively superadditive dependent random variables. Comptes Rendus. Mathématique, Volume 358 (2020) no. 1, pp. 13-21. doi : 10.5802/crmath.7. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.7/

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