×
Shen, Aiting; Wu, Ranchao

Strong and weak convergence for asymptotically almost negatively associated random variables. (English) Zbl 1269.60036

Discrete Dyn. Nat. Soc. 2013, Article ID 235012, 7 p. (2013).
Summary: The strong law of large numbers for sequences of asymptotically almost negatively associated (AANA) random variables is obtained, which generalizes and improves the corresponding one by Z. D. Bai and P. E. Cheng [Stat. Probab. Lett. 46, No. 2, 105–112 (2000; Zbl 0960.60026)] for independent and identically distributed random variables. In addition, the Feller-type weak law of large numbers for sequences of AANA random variables is obtained, which generalizes the corresponding one by W. Feller [Am. J. Math. 68, 257–262 (1946; Zbl 0060.28704)] for independent and identically distributed random variables.

Cited in 15 Documents

MSC:

60F15 Strong limit theorems
60F05 Central limit and other weak theorems

Keywords:

asymptotically almost negatively associated random variables; strong law of large numbers; Feller-type weak law of large numbers

Citations:

Zbl 0960.60026; Zbl 0060.28704
Cite Review PDF
Full Text: DOI
OA License

References:

[1] DOI: 10.1007/BF02218047 · Zbl 0833.60031 · doi:10.1007/BF02218047
[2] Statistica Sinica 7 (4) pp 923– (1997)
[3] Statistics & Probability Letters 46 (2) pp 105– (2000) · Zbl 0960.60026 · doi:10.1016/S0167-7152(99)00093-0
[4] DOI: 10.1590/S0001-37652006000400001 · Zbl 1147.60310 · doi:10.1590/S0001-37652006000400001
[5] DOI: 10.1155/2010/383805 · Zbl 1202.60044 · doi:10.1155/2010/383805
[6] DOI: 10.1007/s00362-009-0241-9 · Zbl 1247.60041 · doi:10.1007/s00362-009-0241-9
[7] DOI: 10.1155/2011/157816 · Zbl 1216.60026 · doi:10.1155/2011/157816
[8] DOI: 10.1016/j.aml.2012.02.069 · Zbl 1251.60025 · doi:10.1016/j.aml.2012.02.069
[9] DOI: 10.1007/BF00114421 · Zbl 0853.60032 · doi:10.1007/BF00114421
[10] DOI: 10.1007/BF02214087 · Zbl 0857.60021 · doi:10.1007/BF02214087
[11] Southeast Asian Bulletin of Mathematics 27 (2) pp 369– (2003)
[12] Taiwanese Journal of Mathematics 9 (1) pp 111– (2005)
[13] DOI: 10.1007/s11425-009-0154-z · Zbl 1184.62099 · doi:10.1007/s11425-009-0154-z
[14] DOI: 10.1155/2010/218380 · Zbl 1207.60025 · doi:10.1155/2010/218380
[15] DOI: 10.1155/2011/717126 · Zbl 1235.60026 · doi:10.1155/2011/717126
[16] Abstract and Applied Analysis (2012)
[17] DOI: 10.1155/2012/562838 · Zbl 1257.62066 · doi:10.1155/2012/562838
[18] Discrete Dynamics in Nature and Society 2012 (2012)
[19] American Journal of Mathematics 68 (2) pp 257– (1946) · Zbl 0060.28704 · doi:10.2307/2371837
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.