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May, 1976 When are the Mean and the Studentized Differences Independent?
Lennart Bondesson
Ann. Statist. 4(3): 668-672 (May, 1976). DOI: 10.1214/aos/1176343477


Let $X_1, \cdots, X_n$ be i.i.d. rv's. Let further $\bar{X} = \sum X_i/n, S^2 = \sum(X_i - \bar{X})^2$, and $U = ((X_1 - \bar{X})/S, \cdots, (X_n - \bar{X})/S)$. If the variables $X_i$ are normally distributed or distributed as linearly transformed Gamma variables, $\bar{X}$ and $U$ are independent. In this paper we show that also the converse must hold.


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Lennart Bondesson. "When are the Mean and the Studentized Differences Independent?." Ann. Statist. 4 (3) 668 - 672, May, 1976.


Published: May, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0328.62008
MathSciNet: MR400491
Digital Object Identifier: 10.1214/aos/1176343477

Primary: 62E10

Keywords: Analytic function , Cauchy's functional equation , Characteristic function , Constant regression

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 3 • May, 1976
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