Asymptotic expansions of convolutions of regularly varying distributions
Asymptotic expansions of convolutions of regularly varying distributions
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DOI：
10.1017/s1446788700008570
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发表时间：
2005-06
影响因子：
0.7
通讯作者：
P. Barbe;W. McCormick
中科院分区：
文献类型：
--
作者：
P. Barbe;W. McCormick
**摘要**：在本文中，我们推导出了任意有限个独立重尾随机变量之和的精确尾区近似值。为了得到二阶渐近性，对具有正则变化尾的分布函数类施加了一个温和的正则性条件。当考虑具有正则变化尾的分布函数的一个半参数子类时，也得到了高阶渐近性。这些半参数子类在卷积运算下是封闭的，并且构建了一个卷积代数，以便根据卷积中组成分布的参数来评估卷积的参数。还给出了一个执行此任务的Maple代码。
Abstract In this paper we derive precise tail-area approximations for the sum of an arbitrary finite number of independent heavy-tailed random variables. In order to achieve second-order asymptotics, a mild regularity condition is imposed on the class of distribution functions with regularly varying tails. Higher-order asymptotics are also obtained when considering asemiparametric subclass of distribution functions with regularly varying tails. These semiparametric subclasses are shown to be closed under convolutions and a convolution algebra is constructed to evaluate the parameters of a convolution from the parameters of the constituent distributions in the convolution. A Maple code is presented which does this task.