let  be a sequence of arbitrary random variables with  and , for every  and  be an array of real numbers. we will obtain two maximal inequalities for partial sums and weighted sums of random variables and also, we will prove complete convergence for weighted sums , under some conditions on  and sequence .

Let  be a sequence of arbitrary random variables with  and , for every  and  be an array of real numbers. We will obtain two maximal inequalities for partial sums and weighted sums of random variables and also, we will prove complete convergence for weighted sums , under some conditions on  and sequence .

Let be a sequence of weakly negative dependent (denoted by, WND) random variables with common distribution function F and let be other sequence of positive random variables independent of and for some and for all . In this paper, we study the asymptotic behavior of the tail probabilities of the maximum, weighted sums, randomly weighted sums and randomly indexed weighted sums of heavy...

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 real numbe...

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...

in this paper, we discuss strong laws for weighted sums of pairwise negatively dependent random variables. the results on i.i.d case of soo hak sung [9] are generalized and extended.

In this paper, we discuss strong laws for weighted sums of pairwise negatively dependent random variables. The results on i.i.d case of Soo Hak Sung [9] are generalized and extended.

‎the main purpose of this note is to establish some bounds in poisson approximation for row-wise arrays of independent geometric distributed random variables using the operator method‎. ‎some results related to random sums of independent geometric distributed random variables are also investigated.

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.

In this paper, we discuss the distributional properties of random sums. We first derive conditions under which the distribution of a binomial sum is PF2 and then show under the same conditions the distribution of a Poisson sum is PF2 by approximating a Poisson sum by a sequence of binomial sums. The PF2 property reveals the monotonicity property of the reversed failure rates of certain compound...