Annals of Mathematical Statistics

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

Cecil Hastings, Jr., Frederick Mosteller, John W. Tukey, and Charles P. Winsor

Full-text: Open access


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

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

First available in Project Euclid: 28 April 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier



Hastings, Cecil; Mosteller, Frederick; Tukey, John W.; Winsor, Charles P. Low Moments for Small Samples: A Comparative Study of Order Statistics. Ann. Math. Statist. 18 (1947), no. 3, 413--426. doi:10.1214/aoms/1177730388.

Export citation