In this paper, we obtain some Rosenthal’s type inequalities for NEGATIVELY orthant DEPENDENT (NOD) RANDOM VARIABLES.

Let { X n≥  1} be a stationary sequence of pair wise negative quadrant DEPENDENT RANDOM VARIABLES with survival function  F( x)=P[X >x]. The empirical survival function Fn(x) based on X1, X2,… X n is proposed as an estimator for Fn ( x). Strong consistency and point wise as well as uniform of Fn (x) are discussed.    

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.  

In this paper, strong laws of large numbers (SLLN) are obtained for the sums Σn i=1Xi , under certain conditions, where {Xn ,n≥1} n is a sequence of pairwise NEGATIVELY DEPENDENT RANDOM VARIABLES.

In this paper, first we obtain some inequalities for the maximum of partial sums ∑nk=1Xn where{Xn ,n≥1} is a sequence of NEGATIVELY DEPENDENT (ND) RANDOM VARIABLES. Then we apply these inequalities to generalized some classical strong limit theorems in probability, if E[Xn │F­n-1]=0, and Fn  =σ(X1 ,X2 ,…Xn), for every n≥1.

In this paper, we will discuss the concept of almost sure convergence for specific groups of fuzzy RANDOM VARIABLES. For this purpose, we use the type of generalized Chebyshev inequalities. Moreover, we show the concept of almost sure convergence of weighted average pairwise NQD of fuzzy RANDOM VARIABLES.

In this paper, we extend and generalize some recent results on the strong laws of large numbers (SLLN) for pairwise inDEPENDENT RANDOM VARIABLES [3]. No assumption is made concerning the existence of independence among the RANDOM VARIABLES (henceforth r.v.’s). Also Chandra’s result on Cesàro uniformly integrable r.v.’s is extended.