## The Annals of Statistics

- Ann. Statist.
- Volume 4, Number 6 (1976), 1244-1246.

### A Characterization of the Asymptotic Normality of Linear Combinations of Order Statistics from the Uniform Distribution

#### Abstract

A necessary and sufficient condition for the asymptotic normality of linear combinations of order statistics from the uniform distribution over [0, 1] is derived. The condition implies, that the variances of all weighted extremes are asymptotically zero compared with the total variance of the sum, which conversely, in the case of nonnegative constants, is sufficient for the asymptotic normality.

#### Article information

**Source**

Ann. Statist., Volume 4, Number 6 (1976), 1244-1246.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176343656

**Digital Object Identifier**

doi:10.1214/aos/1176343656

**Mathematical Reviews number (MathSciNet)**

MR423642

**Zentralblatt MATH identifier**

0345.62033

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62G30: Order statistics; empirical distribution functions

Secondary: 62E20: Asymptotic distribution theory 60F05: Central limit and other weak theorems

**Keywords**

Linear combinations of order statistics asymptotic normality

#### Citation

Hecker, H. A Characterization of the Asymptotic Normality of Linear Combinations of Order Statistics from the Uniform Distribution. Ann. Statist. 4 (1976), no. 6, 1244--1246. doi:10.1214/aos/1176343656. https://projecteuclid.org/euclid.aos/1176343656