The Laws of Large Numbers for Set-Valued Negatively Dependent Random Variables

Abstract

In this paper, we firstly give the definition of set-valued negatively dependent random variables and discuss its properties. Then we proved the weak laws of large numbers for negatively dependent set-valued random variables in the sense of Hausdorff metric. The results are the extension of laws of large numbers for real-valued negatively dependent random variables, and also the extension of LLN for set-valued negatively dependent random variables.