no. 1
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]
Naderi, Habib1  ; Matuła, Przemysław2 ; Salehi, Mahdi3 ; Amini, Mohammad4
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, Tome 358 (2020) no. 1, pp. 13-21.

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.

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Révisé le :
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DOI : 10.5802/crmath.7
Classification : 60F05, 60F15, 65C10
Naderi, Habib 1 ; Matuła, Przemysław 2 ; Salehi, Mahdi 3 ; Amini, Mohammad 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 
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     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},
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Naderi, Habib; Matuła, Przemysław; Salehi, Mahdi; Amini, Mohammad. On weak law of large numbers for sums of negatively superadditive dependent random variables. Comptes Rendus. Mathématique, Tome 358 (2020) no. 1, pp. 13-21. doi : 10.5802/crmath.7. http://www.numdam.org/articles/10.5802/crmath.7/

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