## The Annals of Mathematical Statistics

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

John Gurland

#### 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

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
• 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.