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June, 1946 Some Order Statistic Distributions for Samples of Size Four
John E. Walsh
Ann. Math. Statist. 17(2): 246-248 (June, 1946). DOI: 10.1214/aoms/1177730988


Let $x_1, x_2, x_3, x_4$ represent the values of a sample of size four drawn from a normal population. There is no loss of generality in assuming that the distribution function of this population has zero mean and unit vriance. Denote it by $N(0, 1)$. Let $x_(i)$ be the ith largest of $x_1, x_2, x_3, x_4$. The purpose of this note is to determine the joint distribution of $x{(4)} + x_{(3)} - x_{(2)} - x_{(1)}, x_{(4)} - x_{(3)} + x_{(2)} -x_{(1)}$, and $x_{(4)} - x_{(3)} - x_{(2)} + x_{(1)}$, and derive from this joint distribution the joint distributions of these statistics taken in pairs, also the distribution of each statistic itself.


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John E. Walsh. "Some Order Statistic Distributions for Samples of Size Four." Ann. Math. Statist. 17 (2) 246 - 248, June, 1946.


Published: June, 1946
First available in Project Euclid: 28 April 2007

zbMATH: 0060.30014
MathSciNet: MR16616
Digital Object Identifier: 10.1214/aoms/1177730988

Rights: Copyright © 1946 Institute of Mathematical Statistics

Vol.17 • No. 2 • June, 1946
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