Journal of Applied Mathematics and Decision Sciences
Volume 5 (2001), Issue 3, Pages 181-191

Power of the Neyman smooth tests for the uniform distribution

Glen D. Rayner1 and John C. W. Rayner2

1School of Computing and Mathematics, Deakin University, Waurn Ponds, VIC3217, Australia
2School of Mathematics and Applied Statistics, University of Wollongong, NSW2522, Australia

Copyright © 2001 Glen D. Rayner and John C. W. Rayner. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper compares and investigates the generalised Neyman smooth test, its components, and the classical chi-squared test with a variety of equiprobable classes. Each test is evaluated in terms of its power to reject a wavelike alternative to the uniform distribution, chosen to quantify the complexity of the alternative. Results indicate that if broadly focused tests (rather than strongly directional or weakly omnibus) are sought, then smooth tests of order about four, or the chi-squared test with between five and ten classes, will perform well.