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September, 1952 On a the Test for Homogeneity and Extreme Values
D. A. Darling
Ann. Math. Statist. 23(3): 450-456 (September, 1952). DOI: 10.1214/aoms/1177729390


Let $x_1, x_2, \cdots, x_n$ be positive, identically distributed, independent random variables. It is of some statistical interest to study the distribution of $z_n = (x_1 + x_2 + \cdots + x_n)/\max (x_1, x_2, \cdots, x_n)$. In this paper we give its characteristic function and in a few cases its distribution. A limiting distribution of fairly wide applicability is given in the last section.


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D. A. Darling. "On a the Test for Homogeneity and Extreme Values." Ann. Math. Statist. 23 (3) 450 - 456, September, 1952.


Published: September, 1952
First available in Project Euclid: 28 April 2007

zbMATH: 0049.10001
MathSciNet: MR50236
Digital Object Identifier: 10.1214/aoms/1177729390

Rights: Copyright © 1952 Institute of Mathematical Statistics

Vol.23 • No. 3 • September, 1952
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