On Tail Categorization of Probability Laws
提出一种不依赖光滑性条件的概率律尾部分类方案，根据分布函数F(ln x)的变异性将尾部划分为长尾、中尾和短尾，并建立与极端间距极限行为及矩存在性的联系。
Abstract A classification scheme for probability laws by tail behavior is proposed. It circumvents the smoothness conditions usually imposed on the probability laws by current classification schemes and yields a complete characterization of the probability distributions belonging to each category. That is, a distribution function F has a long, medium, or short tail, depending on whether F (ln x) is slowly varying, regularly varying, or rapidly varying. A clear and concise connection with the limiting behavior of extreme spacings is also established and the connection with the existence of moments and moment generating functions is noted. Closure properties of the classification scheme under reliability operations are also considered.