Conditional Acceptability for Random Variables

Abstract

Acceptable random variables introduced by Giuliano Antonini et al. (J. Math. Anal. Appl. 338:1188-1203, 2008) form a class of dependent random variables that contains negatively dependent random variables as a particular case. The concept of
acceptability has been studied by authors under various versions of the definition, such as extended acceptability or wide acceptability. In this paper, we combine the concept of acceptability with the concept of conditioning, which has been the
subject of current research activity. For conditionally acceptable random variables, we provide a number of probability inequalities that can be used to obtain asymptotic results.