Complete Convergence forWeighted Sums of Negatively Superadditive Dependent Random Variables
نویسندگان
چکیده
Abstract. Let {Xn,n≥1} be a sequence of negatively superadditive dependent (NSD, in short) random variables and {ank,1≤ k≤n,n≥1} be an array of real numbers. Under some suitable conditions, we present some results on complete convergence for weighted sums ∑k=1ankXk of NSD random variables by using the Rosenthal type inequality. The results obtained in the paper generalize some corresponding ones for independent random variables and negatively associated random variables.
منابع مشابه
On the complete convergence of weighted sums for an array of rowwise negatively superadditive dependent random variables
ABSTRACT: In this paper, the complete convergence and the complete moment convergence of weighted sums for an array of negatively superadditive dependent random variables are established. The results generalize the Baum-Katz theorem on negatively superadditive dependent random variables. In particular, the Marcinkiewicz-Zygmund type strong law of large numbers of weights sums for sequences of n...
متن کاملOn the Complete Convergence ofWeighted Sums for Dependent Random Variables
We study the limiting behavior of weighted sums for negatively associated (NA) random variables. We extend results in Wu (1999) and a theorem in Chow and Lai (1973) for NA random variables.
متن کاملStrong Convergence of Weighted Sums for Negatively Orthant Dependent Random Variables
We discuss in this paper the strong convergence for weighted sums of negatively orthant dependent (NOD) random variables by generalized Gaussian techniques. As a corollary, a Cesaro law of large numbers of i.i.d. random variables is extended in NOD setting by generalized Gaussian techniques.
متن کاملThe Almost Sure Convergence for Weighted Sums of Linear Negatively Dependent Random Variables
In this paper, we generalize a theorem of Shao [12] by assuming that is a sequence of linear negatively dependent random variables. Also, we extend some theorems of Chao [6] and Thrum [14]. It is shown by an elementary method that for linear negatively dependent identically random variables with finite -th absolute moment the weighted sums converge to zero as where and is an array of...
متن کاملOn the strong convergence for weighted sums of negatively superadditive dependent random variables
In this article, some strong convergence results for weighted sums of negatively superadditive dependent random variables are studied without assumption of identical distribution. The results not only generalize the corresponding ones of Cai (Metrika 68:323-331, 2008) and Sung (Stat. Pap. 52:447-454, 2011), but also extend and improve the corresponding one of Chen and Sung (Stat. Probab. Lett. ...
متن کامل