## The Annals of Mathematical Statistics

### Estimates of the Mean and Standard Deviation of a Normal Population

W. J. Dixon

#### Abstract

Several simple estimates of the mean and standard deviation of a normal population are discussed. The efficiencies of these estimates are compared to the sample mean and sample standard deviation and to the best linear unbiased estimates. Little efficiency is lost when simple rather than optimum weights are used. Since moments of the order statistics are now available for samples of sizes $N \leqq 20$ from normal populations [3] it is a simple matter to find the variances of linear combinations of order statistics. The sample values are denoted $X_1 \leqq X_2 \leqq X_3 \leqq \cdots \leqq X_N$.

#### Article information

Source
Ann. Math. Statist., Volume 28, Number 3 (1957), 806-809.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177706898

Digital Object Identifier
doi:10.1214/aoms/1177706898

Mathematical Reviews number (MathSciNet)
MR91590

Zentralblatt MATH identifier
0082.13605

JSTOR
links.jstor.org

#### Citation

Dixon, W. J. Estimates of the Mean and Standard Deviation of a Normal Population. Ann. Math. Statist. 28 (1957), no. 3, 806--809. doi:10.1214/aoms/1177706898. https://projecteuclid.org/euclid.aoms/1177706898