On almost sure convergence for weighted sums of pairwise negatively quadrant dependent random variables

Let {X <Subscript> n </Subscript>, n ≥ 1} be a sequence of pairwise negatively quadrant dependent (NQD) random variables. In this study, we prove almost sure limit theorems for weighted sums of the random variables. From these results, we obtain a version of the Glivenko–Cantelli lemma for pairwise NQD random variables under some fragile conditions. Moreover, a simulation study is done to compare the convergence rates with those of Azarnoosh (Pak J Statist 19(1):15–23, <CitationRef CitationID="CR2">2003</CitationRef>) and Li et al. (Bull Inst Math 1:281–305, <CitationRef CitationID="CR12">2006</CitationRef>). Copyright Springer-Verlag 2013