## The Annals of Mathematical Statistics

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

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

#### 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

#### 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.Project Euclid: euclid.aoms/1177693263

#### 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.Project Euclid: euclid.aoms/1177706116