## The Annals of Mathematical Statistics

### Low Moments for Small Samples: A Comparative Study of Order Statistics

#### Abstract

The means, variances, and covariances for samples of size $\leq 10$ from the normal distribution, a selected long-tailed distribution, and the uniform distribution are tabled and compared with the usual asymptotic approximations. The methods of computation used and the accuracy expected are discussed. Use is made of the representation of an arbitrarily distributed variate as a monotone function of a uniformly (rectangularly) distributed variate. It is hoped that these tables will encourage experimentation with new statistical procedures.

#### Article information

Source
Ann. Math. Statist., Volume 18, Number 3 (1947), 413-426.

Dates
First available in Project Euclid: 28 April 2007

https://projecteuclid.org/euclid.aoms/1177730388

Digital Object Identifier
doi:10.1214/aoms/1177730388

Mathematical Reviews number (MathSciNet)
MR22335

Zentralblatt MATH identifier
0034.07401

JSTOR