## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 28, Number 3 (1957), 786-790.

### The Distribution of the Number of Locally Maximal Elements in a Random Sample

T. Austin, R. Fagen, T. Lehrer, and W. Penney

#### Abstract

The distribution of the number of different locally maximal elements in a random sample is found, where the sampling is from a continuous population of real numbers. This distribution has application in certain nonparametric tests; the problem of finding the distribution may be regarded as identical with the enumeration of permutations according to the number of distinct locally maximal elements.

#### Article information

**Source**

Ann. Math. Statist., Volume 28, Number 3 (1957), 786-790.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177706893

**Digital Object Identifier**

doi:10.1214/aoms/1177706893

**Mathematical Reviews number (MathSciNet)**

MR91251

**Zentralblatt MATH identifier**

0078.01001

**JSTOR**

links.jstor.org

#### Citation

Austin, T.; Fagen, R.; Lehrer, T.; Penney, W. The Distribution of the Number of Locally Maximal Elements in a Random Sample. Ann. Math. Statist. 28 (1957), no. 3, 786--790. doi:10.1214/aoms/1177706893. https://projecteuclid.org/euclid.aoms/1177706893