New examples of heavy-tailed O-subexponential distributions and related closure properties

Let LL and SS denote the classes of distributions with long tails and subexponential tails respectively. Let OSOS denote the class of distributions with O-subexponential tails, which means the distributions with the tails having the same order as the tails of their 2-fold convolutions. In this paper, we first construct a family of distributions without finite means in L∩OS∖SL∩OS∖S. Next some distributions in L∩OS∖SL∩OS∖S, which possess finite means or even finite higher moments, are also constructed. In connection with this, we prove that the class OSOS is closed under minimization of random variables. However, it is not closed under maximization of random variables.