中文摘要：

本文利用Cline和Samorodnitsky（1994）的方法。讨论了长尾分布族及其相关分布族的若干性质。在此基础上，分别获得了一类次指数分布族及其相关的分布族的充分条件和必要条件．

英文摘要：

In this paper, we use the method of Cline and Samorodnitsky（1994） to discuss the properties of the long-tailed disrtibution and its related distribution. On the basis of this study, we obtain the sufficient condition and the necessary condition of a class of subexponential distribution and its related distributions.