Annals of Mathematical Statistics

Some Order Statistic Distributions for Samples of Size Four

John E. Walsh

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Abstract

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.

Article information

Source
Ann. Math. Statist., Volume 17, Number 2 (1946), 246-248.

Dates
First available in Project Euclid: 28 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177730988

Digital Object Identifier
doi:10.1214/aoms/1177730988

Mathematical Reviews number (MathSciNet)
MR16616

Zentralblatt MATH identifier
0060.30014

JSTOR
links.jstor.org

Citation

Walsh, John E. Some Order Statistic Distributions for Samples of Size Four. Ann. Math. Statist. 17 (1946), no. 2, 246--248. doi:10.1214/aoms/1177730988. https://projecteuclid.org/euclid.aoms/1177730988


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