Journal of Applied Mathematics and Decision Sciences
Volume 5 (2001), Issue 1, Pages 1-19

One sample tests for the location of modes of nonnormal data

Anthony M. Carolan and J. C. W. Rayner

School of Mathematics and Applied Statistics, University of Wollongong, Australia

Copyright © 2001 Anthony M. Carolan and J. 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.


There are few techniques available for testing if modes take specified values. We show that standard tests of location such as the t-test and the Wilcoxon test, which test for the mean and median respectively, can perform poorly as tests for modes when the data is other than unimodal and symmetric. Carolan and Rayner [1] proposed a score test of location for symmetric nonnormal data. We consider a family of distributions similar to those considered by Carolan and Rayner [1] and propose a test for the mode or modes of data from multimodal or skewed distributions and demonstrate by way of simulations that it is reasonably effective.