Complete convergence for weighted sums of arrays of APND random variables

In this note, we introduce a new class of dependent random variables (henceforth rvs), together with some its basic properties. This class includes independent rvs and pairwise negatively dependent rvs. Some extensions of Ranjbar et al. (2008) are discussed. The complete convergence for the new class of rvs is also proved, and some results of Beak and Park (2010 Beak, J.-II., and S. T. Park. 2010. Convergence of weighted sums for arrays of negatively dependent random variables and its applications. J. Stat. Plann. Inference 140:2461–2469.[Crossref], [Web of Science ®] , [Google Scholar]) are extended to this class conveniently.