Comptes Rendus
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]
Habib Naderi1  ; Przemysław Matuła2 ; Mahdi Salehi3 ; Mohammad Amini4
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.

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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DOI : 10.5802/crmath.7
Classification : 60F05, 60F15, 65C10
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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     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},
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     doi = {10.5802/crmath.7},
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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/

[1] André Adler; Przemysław Matuła On exact strong laws of large numbers under general dependence conditions, Probab. Math. Stat., Volume 38 (2018) no. 1, pp. 103-121 | MR | Zbl

[2] Khursheed Alam; K. M. Lal Saxena Positive dependence in multivariate distributions, Commun. Stat., Theory Methods, Volume 10 (1981), pp. 1183-1196 | DOI | MR | Zbl

[3] Nicholas H. Bingham; Charles M. Goldie; Jozef L. Teugels Regular variation, Encyclopedia of Mathematics and Its Applications, 27, Cambridge University Press, 1987 | MR | Zbl

[4] Henry W. Block; Thomas H. Savits; Moshe Shaked Some concepts of negative dependence, Ann. Probab., Volume 10 (1982), pp. 765-772 | DOI | MR | Zbl

[5] Alexander Bulinski; Alexey Shashkin Limit theorems for associated random fields and related systems, Advanced Series on Statistical Science & Applied Probability, 10, World Scientific, 2007 | DOI | MR | Zbl

[6] Tasos C. Christofides; Eutichia Vaggelatou A connection between supermodular ordering and positive/negative association, J. Multivariate Anal., Volume 88 (2004) no. 1, pp. 138-151 | DOI | MR | Zbl

[7] István Fazekas; Przemysław Matuła; Maciej Ziemba A note on the weighted strong law of large numbers under general conditions, Publ. Math., Volume 90 (2017) no. 3-4, pp. 373-386 | MR | Zbl

[8] Taizhong Hu Negatively superadditive dependence of random variables with applications, Chin. J. Appl. Probab. Stat., Volume 16 (2000) no. 2, pp. 133-144 | MR | Zbl

[9] Ryszard Jajte On the strong law of large numbers, Ann. Probab., Volume 31 (2003) no. 1, pp. 409-412 | MR | Zbl

[10] Kumar Joag-Dev; Frank Proschan Negative association of random variables with applications, Ann. Stat., Volume 11 (1983), pp. 286-295 | DOI | MR | Zbl

[11] Colin L. Mallows; Donald Richter Inequalities of Chebyshev type involving conditional expectations, Ann. Math. Stat., Volume 40 (1969), pp. 1922-1932 | DOI | MR | Zbl

[12] H. Naderi; Przemysław Matuła; M. Amini; H. Ahmadzade A version of the Kolmogorov–Feller weak law of large numbers for maximal weighted sums of random variables, Commun. Stat., Theory Methods, Volume 48 (2018) no. 21, pp. 5414-5418 | DOI

[13] Habib Naderi; Przemysław Matuła; Mohammad Amini; Abolghasem Bozorgnia On stochastic dominance and the strong law of large numbers for dependent random variables, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM, Volume 110 (2016) no. 2, pp. 771-782 | DOI | MR | Zbl

[14] Valentin V. Petrov Limit theorems of probability theory. Sequences of independent random variables, Oxford Studies in Probability, 4, Clarendon Press, 1995 | MR | Zbl

[15] Aiting Shen On the strong law of large numbers for weighted sums of negatively superadditive dependent random variables, J. Korean Math. Soc., Volume 53 (2016) no. 1, pp. 45-55 | DOI | MR | Zbl

[16] Demei Yuan; Xuemei Hu A conditional version of the extended Kolmogorov-Feller weak law of large numbers, Stat. Probab. Lett., Volume 97 (2015), pp. 99-107 | DOI | MR | Zbl

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