短尾对称分布序列极值的渐近性质
发布时间：2019-02-23 12:16
【摘要】：本文主要研究在线性赋范和幂赋范下,服从短尾对称分布的独立同分布随机变量序列的渐进性质,以及线性赋范下短尾对称分布极值矩的收敛速度.文章主要包括三部分内容:第一部分,首先根据短尾对称分布的概率密度函数推导出该分布的尾部表达式,并判断出该分布的极值分布类型.在线性赋范下,通过对尾部表达式的精确展开,得到其规范化最大值的极值分布的渐进展开式以及其收敛到极值分布的收敛速度.第二部分,在幂赋范下,利用类似的方法研究得到了其规范化最大值的极值分布的渐进展开式以及其收敛到极值分布的收敛速度.第三部分,在规范化局部最大值的分布的渐进展开式的基础上,通过分布矩的定义以及相应控制条件,得到了短尾对称分布的局部最大值的矩的渐进展开式以及其收敛到极值分布的收敛速度.
[Abstract]:In this paper, we study the asymptotic properties of the sequence of independent homomorphic random variables under linear normed and power normed distributions, and the convergence rate of extreme moments of short-tailed symmetric distributions under linear normed. This paper mainly includes three parts: in the first part, according to the probability density function of the short-tailed symmetric distribution, the tail expression of the distribution is derived, and the extreme distribution type of the distribution is determined. By the exact expansion of the tail expression under linear normed, the asymptotic expansion of the extreme value distribution of its normalized maximum value and the convergence rate of its convergence to the extreme value distribution are obtained. In the second part, the asymptotic expansion of the extreme value distribution of its normalized maximum value and the convergence rate of its convergence to the extreme value distribution are obtained by using a similar method under the power norm. In the third part, on the basis of the asymptotic expansion of the distribution of the normalized local maximum value, the definition of the distribution moment and the corresponding control conditions are adopted. The asymptotic expansion of the moment of the local maximum of the short-tailed symmetric distribution and the convergence rate of its convergence to the extremum distribution are obtained.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211
本文编号：2428810
[Abstract]:In this paper, we study the asymptotic properties of the sequence of independent homomorphic random variables under linear normed and power normed distributions, and the convergence rate of extreme moments of short-tailed symmetric distributions under linear normed. This paper mainly includes three parts: in the first part, according to the probability density function of the short-tailed symmetric distribution, the tail expression of the distribution is derived, and the extreme distribution type of the distribution is determined. By the exact expansion of the tail expression under linear normed, the asymptotic expansion of the extreme value distribution of its normalized maximum value and the convergence rate of its convergence to the extreme value distribution are obtained. In the second part, the asymptotic expansion of the extreme value distribution of its normalized maximum value and the convergence rate of its convergence to the extreme value distribution are obtained by using a similar method under the power norm. In the third part, on the basis of the asymptotic expansion of the distribution of the normalized local maximum value, the definition of the distribution moment and the corresponding control conditions are adopted. The asymptotic expansion of the moment of the local maximum of the short-tailed symmetric distribution and the convergence rate of its convergence to the extremum distribution are obtained.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211
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