The Annals of Mathematical Statistics

Distribution of the Maximum of the Arithmetic Mean of Correlated Random Variables

John Gurland

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Abstract

The initial distribution considered here is obtained from a multivariate analogue of the Pearson Type III distribution, and the value of the correlation is taken to be non-negative. There is obtained here the distribution of the maximum in samples of fixed size $n$ from a random variable which is the arithmetic mean of $k$ such correlated random variables. This distribution is obtained for large values of $n$ and for large values of $k$. The appropriate expressions for the mode and scale parameters are also given.

Article information

Source
Ann. Math. Statist., Volume 26, Number 2 (1955), 294-300.

Dates
First available in Project Euclid: 28 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177728546

Digital Object Identifier
doi:10.1214/aoms/1177728546

Mathematical Reviews number (MathSciNet)
MR93067

Zentralblatt MATH identifier
0065.11904

JSTOR
links.jstor.org

Citation

Gurland, John. Distribution of the Maximum of the Arithmetic Mean of Correlated Random Variables. Ann. Math. Statist. 26 (1955), no. 2, 294--300. doi:10.1214/aoms/1177728546. https://projecteuclid.org/euclid.aoms/1177728546


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See also

  • Later Acknowledgment of Priority: S. A. Patil, S. H. Liao. Acknowledgment of Priority to: ``The Distribution of the Ratio of Means to the Square Root of the Sum of Variances of a Bivariate Normal Sample''. Ann. Math. Statist., Volume 42, Number 4 (1971), 1461--1461.

Corrections

  • See Correction: John Gurland. Correction Notes: Corrections to "Distribution of the Maximum of the Arithmetic Mean of Correlated Random Variables". Ann. Math. Statist., Volume 30, Number 4 (1959), 1265--1266.