中文摘要：

作为正态分布的推广,广义误差分布是在统计中是应用最广泛的分布之一。有限混合分布在现代统计中的整个发展过程中作为一个模型得到了广泛的研究和应用.这篇文章在广义误差分布的一个重要不等式的基础上研究了有限混合广义误差分布的尾部性质,得到了它的尾部的渐近性质,同时得到了Mill’s率。然后利用有限混合广义误差分布的尾部渐近性质讨论了同服从该分布的独立随机变量序列最大值的极限分布以及如何选择适当的的规范化常数使得最大值的分布收敛到双指数分布。

英文摘要：

The general error distribution being a generalization of normal distribution is one of the most widely applied dis- tributions in statistics. Finite mixture distribution as a model has been widely studied and applied in throughout the devel- opment process of modern statistics. In this paper, based on an inequality of the general error distribution, the asymptotic tail behavior of finite mixture general error distribution is studied and the asymptotic behavior of the tail of this distribution is derived while Mills＇ ratio is obtained. Then, an application of the asymptotic property of the tail of the distribution to consider the limiting distribution of the extreme of independent identically distributed （i. i. d. ） random variable sequence with finite mixed general error distribution and how to choose the suitable normalized constants such that the distribution of maxima converges to double exponential distribution.