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

作者：Lin Jianxi^*; Wang Yuebao

来源：Statistics & Probability Letters, 2012, 82(3): 427-432.

DOI：10.1016/j.spl.2011.12.011

• O-subexponential distribution
• Long-tailed distribution
• Subexponential distribution
• Heavy-tailed distribution
• Closure property

Let L and S denote the classes of distributions with long tails and subexponential tails respectively. Let O S 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 boolean AND O S \ S. Next some distributions in L boolean AND O S \ S, which possess finite means or even finite higher moments, are also constructed. In connection with this, we prove that the class O S is closed under minimization of random variables. However, it is not closed under maximization of random variables.

• 出版日期2012-3
• 单位厦门大学; 苏州大学