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.
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.
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Habib Naderi 1; Przemysław Matuła 2; Mahdi Salehi 3; Mohammad Amini 4
@article{CRMATH_2020__358_1_13_0, 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}, }
TY - JOUR AU - Habib Naderi AU - Przemysław Matuła AU - Mahdi Salehi AU - Mohammad Amini TI - On weak law of large numbers for sums of negatively superadditive dependent random variables JO - Comptes Rendus. Mathématique PY - 2020 SP - 13 EP - 21 VL - 358 IS - 1 PB - Académie des sciences, Paris DO - 10.5802/crmath.7 LA - en ID - CRMATH_2020__358_1_13_0 ER -
%0 Journal Article %A Habib Naderi %A Przemysław Matuła %A Mahdi Salehi %A Mohammad Amini %T On weak law of large numbers for sums of negatively superadditive dependent random variables %J Comptes Rendus. Mathématique %D 2020 %P 13-21 %V 358 %N 1 %I Académie des sciences, Paris %R 10.5802/crmath.7 %G en %F CRMATH_2020__358_1_13_0
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] 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] Positive dependence in multivariate distributions, Commun. Stat., Theory Methods, Volume 10 (1981), pp. 1183-1196 | DOI | MR | Zbl
[3] Regular variation, Encyclopedia of Mathematics and Its Applications, 27, Cambridge University Press, 1987 | MR | Zbl
[4] Some concepts of negative dependence, Ann. Probab., Volume 10 (1982), pp. 765-772 | DOI | MR | Zbl
[5] Limit theorems for associated random fields and related systems, Advanced Series on Statistical Science & Applied Probability, 10, World Scientific, 2007 | DOI | MR | Zbl
[6] A connection between supermodular ordering and positive/negative association, J. Multivariate Anal., Volume 88 (2004) no. 1, pp. 138-151 | DOI | MR | Zbl
[7] 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] Negatively superadditive dependence of random variables with applications, Chin. J. Appl. Probab. Stat., Volume 16 (2000) no. 2, pp. 133-144 | MR | Zbl
[9] On the strong law of large numbers, Ann. Probab., Volume 31 (2003) no. 1, pp. 409-412 | MR | Zbl
[10] Negative association of random variables with applications, Ann. Stat., Volume 11 (1983), pp. 286-295 | DOI | MR | Zbl
[11] Inequalities of Chebyshev type involving conditional expectations, Ann. Math. Stat., Volume 40 (1969), pp. 1922-1932 | DOI | MR | Zbl
[12] 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] 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] Limit theorems of probability theory. Sequences of independent random variables, Oxford Studies in Probability, 4, Clarendon Press, 1995 | MR | Zbl
[15] 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] 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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