| 渐近正态随机变量函数的极限分布 |
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| 引用本文： | 牛司丽,刘玉晓.渐近正态随机变量函数的极限分布[J].大学数学,2021,37(2):48-52. |
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| 作者姓名： | 牛司丽 刘玉晓 |
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| 作者单位： | 同济大学 数学科学学院,上海 200092;河南城建学院 数理学院,河南 平顶山 467036 |
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| 摘 要： | 基于渐近正态随机变量,导出随机变量函数极限分布的两个一般性理论结果.作为应用,证明了渐近正态随机变量一系列具体函数的极限分布,其中包括泊松随机变量平方根的渐近正态性,以及随机变量部分和在正则化常数是随机变量情况下的渐近正态性.
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| 关 键 词： | 随机变量的函数 极限分布 渐近正态随机变量 泊松随机变量 |
Limit Distribution of Function of Asymptotic Normal Random Variable |
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| NIU Si-li,LIU Yu-xiao.Limit Distribution of Function of Asymptotic Normal Random Variable[J].College Mathematics,2021,37(2):48-52. |
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| Authors: | NIU Si-li LIU Yu-xiao |
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| Institution: | (School of Mathematical Sciences,Tongji University,Shanghai 200092,China;School of Mathematics and Physics,Henan University of Urban Construction,Pingdingshan Henan 467036,China) |
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| Abstract: | Based on asymptotic normal random variable,two general theoretical results of limit distribution of function of random variable are derived.As application,the limit distributions of a series of specific functions of the asymptotic normal random variables are proved,where the limit distributions include the asymptotic normality of the square root for Poisson random variables and the asymptotic normality of partial sum of random variables when the regularization constant is a random variable. |
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| Keywords: | function of random variable limit distribution asymptotic normal random variable Poisson random variable |
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