A characterization of the normal distribution by the independence of a pair of random vectors

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• 作者：Wiktor Ejsmont ^{wiktor.ejsmont@ue.wroc.pl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 46L54 ; secondary ; 62E10
• 刊名：Statistics & Probability Letters
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：114
• 期：Complete
• 页码：1-5
• 全文大小：347 K

文摘

Kagan and Shalaevski (1967) have shown that if the random variables X₁,…,X_n${\mathbb{X}}_1,\dots ,{\mathbb{X}}_n$ are i.i.d. and the distribution of ${\sum }_{i=1}^n{({\mathbb{X}}_i+a_i)}^2$46ed9797b1d0f97" title="Click to view the MathML source">a_i∈R$a_i\in \mathbb{R}$ depends only on ${\sum }_{i=1}^n{a}_i^2$, then each X_i∼N(0,σ)${\mathbb{X}}_i\sim N(0,\sigma )$. In this paper, we will give other characterizations of the normal distribution which are formulated in a similar spirit.