Inequalities for random variables

... presented by Yang for NA random variables and Wang et al. for NOD random variables. Using the exponential inequalities, we further study the complete convergence for acceptable random variables. MSC(2000): ... Yang [9] for NA random variables and Wang et al. [10] for NOD random variables. In Section 3, we will study the complete convergence for acceptable rando...

Ngày tải lên: 18/06/2014, 15:20

... inequality for acceptable random variables generalizes and improves the corresponding results presented by Yang for NA random variables and Wang et al. for NOD random variables. Using the exponential inequalities, ... Lemma 3.5] for NA random variables and Wang et al. [10, Theorem 2.3] for NOD random variables. In the following, we will provide the Hoeffding-type...

Ngày tải lên: 20/06/2014, 23:20

... exponential inequalities for positively associated random variables without the boundedness assumption. These inequalities improve the corresponding results obtained by Oliveira 2005. By one of the inequalities, ... exponential inequalities and moment inequalities for partial sum  n i1 X i − EX i  play a very important role in various proofs of limit theorems. For pos...

Ngày tải lên: 21/06/2014, 22:20

... below). For information about publishing your research in Journal of Inequalities and Applications go to http://www.journalofinequalitiesandapplications.com/authors/instructions/ For information ... o(x α−2 l(x)) for α > 2. Lemma 2.2. Let {ξ, ξ n } n∈N be a sequence of uniformly bounded random variables. If exist constants c > 0 and δ > 0 such that |Eξ k ξ j | ≤ c  k j ...

Ngày tải lên: 20/06/2014, 21:20

... sequence of random variables {X n ; n ≥ 1} is said to be pairwise NQD random vari- ables if for all i ≠ j , i, j Î N, X i and X j are NQD random variables. Obviously,asequenceofpairwiseNQDrandom variables ... dependent (NQD) random variables. The concept of NQD random variables was introduced by Lehmann [1]. Definition 1.1 [1] Two random variables X and Y are said to...

Ngày tải lên: 20/06/2014, 22:20

... numbers for sequences of ran- dom variables to the case of triangular array of random variables and arrays of rowwise random variables. For more details about the strong law of large numbers for ... inequality for negatively dependent random variables. Pakistan J Stat. 18, 249–254 (2002) 5. Asadian, N, Fakoor, V, Bozorgnia, A: Rosental’s type inequalities for negativel...

Ngày tải lên: 20/06/2014, 22:20

... asso- ciated and negatively dependent mean zero random variables. The f ollowing lemma is an exponential inequality for negatively d ependent random variables which was proved by Dehua et al. [10] ... random vari- ables with EX i =0and EX 2 i < ∞ for 1 ≤ i ≤ n and let B n =  n i=1 EX 2 i . Then, for any x Sung Journal of Inequalities and Applications 2011, 2011:76 http:/...

Ngày tải lên: 20/06/2014, 22:20

... and Rempala 5 gave an ASCLT for product of partial sums of i.i.d. random variables as follows. Theorem 1.1. Let {X n ,n ≥ 1} be a sequence of i.i.d. positive random variables with EX 1  μ>0 and ... function of the random variable e N , and N is a standard normal variable. Recently, Jin 6 had p roved that 1.1 holds under appropriate conditions for strongly mixing positi...

Ngày tải lên: 21/06/2014, 05:20

... limit theorems for negatively dependent random variable, Ph.D. thesis, 2000. 6 V. Fakoor and H. A. Azarnoosh, “Probability inequalities for sums of negatively dependent random variables, ” Pakistan ... dependent random samples,” Communications in Statistics: Theory and Methods, accepted. 10 Q. Y. Wu, “Complete convergence for negatively dependent sequences of random vari...

Ngày tải lên: 21/06/2014, 07:20

... theorem for dependent random variables, ” Theory of Probability and Its Applications, vol. 20, pp. 134–139, 1975. 3 M. Peligrad, “On the central limit theorem for ρ-mixing sequences of random variables, ” ... {X i ; m ≤ i ≤ n}. The ρ-mixing random variables were first introduced by Kolmogorov and Rozanov 1. The limiting behavior of ρ-mixing random variables is very rich,...

Ngày tải lên: 21/06/2014, 07:20