zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
An exponential inequality for a NOD sequence and a strong law of large numbers. (English) Zbl 1205.60068
Summary: We establish an exponential inequality for unbounded negatively orthant dependent (NOD) random variables. The inequality extends and improves the results of T. S. Kim and H. C. Kim [Commun. Korean Math. Soc. 22, No. 2, 315–321(2007; Zbl 1168.60335)], H. J. Nooghabi and H. A. Azarnoosh [Stat. Pap. 50, No. 2, 419–428 (2009; Zbl 1247.60039)], and G. D. Xing, S. C. Yang, A. L. Liu and X. P. Wang, J. Korean Stat. Soc. 38, No. 1, 53–57 (2009)]. We also obtain the convergence rate O(n -1/2 ln 1/2 n) for the strong law of large numbers, which improves on the corresponding ones of Kim and Kim [loc. cit.], Nooghabi and Azarnoosh (2009), and Xing, Yang, Liu and Wang [loc. cit.].
MSC:
60F15Strong limit theorems
References:
[1]Kim, T. S.; Kim, H. C.: On the exponential inequality for negative dependent sequence, Communications of the korean mathematical society 22, No. 2, 315-321 (2007) · Zbl 1168.60335 · doi:10.4134/CKMS.2007.22.2.315
[2]Nooghabi, H. J.; Azarnoosh, H. A.: Exponential inequality for negatively associated random variables, Statistical papers 50, No. 2, 419-428 (2009)
[3]Xing, G. D.; Yang, S. C.; Liu, A. L.; Wang, X. P.: A remark on the exponential inequality for negatively associated random variables, Journal of the korean statistical society 38, 53-57 (2009)
[4]Sung, S. H.: An exponential inequality for negatively associated random variables, Journal of inequalities and applications 2009, 7 pages (2009) · Zbl 1181.60049 · doi:10.1155/2009/649427
[5]Christofides, T. C.; Hadjikyriakou, M.: Exponential inequalities for N-demimartingales and negatively associated random variables, Statistics probability letters 79, 2060-2065 (2009) · Zbl 1180.60016 · doi:10.1016/j.spl.2009.06.013
[6]Jabbari, H.; Jabbari, M.; Azarnoosh, H. A.: An exponential inequality for negatively associated random variables, Electronic journal of statistics 3, 165-175 (2009)
[7]Joag-Dev, K.; Proschan, F.: Negative association of random variables with applications, The annals of statistics 11, No. 1, 286-295 (1983) · Zbl 0508.62041 · doi:10.1214/aos/1176346079
[8]Ko, M. H.; Kim, T. S.: Almost sure convergence for weighted sums of negatively orthant dependent random variables, Journal of the korean mathematical society 42, No. 5, 949-957 (2005) · Zbl 1096.60017 · doi:10.4134/JKMS.2005.42.5.949
[9]Fakoor, V.; Azarnoosh, H. A.: Probability inequalities for sums of negatively dependent random variables, Pakistan journal of statistics 21, No. 3, 257-264 (2005) · Zbl 1129.60303
[10]Ko, M. H.; Han, K. H.; Kim, T. S.: Strong laws of large numbers for weighted sums of negatively dependent random variables, Journal of the korean mathematical society 43, No. 6, 1325-1338 (2006) · Zbl 1108.60020 · doi:10.4134/JKMS.2006.43.6.1325
[11]Kim, H. C.: The hájek–Rényi inequality for weighted sums of negatively orthant dependent random variables, International journal of contemporary mathematical sciences 1, No. 6, 297-303 (2006) · Zbl 1156.60306
[12]Wu, Q. Y.: Complete convergence for negatively dependent sequences of random variables, Journal of inequalities and applications 2010, 10 pages (2010) · Zbl 1202.60050 · doi:10.1155/2010/507293
[13]Bozorgnia, A.; Patterson, R. F.; Taylor, R. L.: Limit theorems for dependent random variables, , 1639-1650 (1996) · Zbl 0845.60010
[14]Oliveira, P. E.: An exponential inequality for associated variables, Statistics probability letters 73, 189-197 (2005)