Table of Contents
Advances in Statistics
Volume 2014, Article ID 740831, 6 pages
Research Article

Statistical Test for Bivariate Uniformity

Department of Mathematics and Statistics, Florida International University, Miami, FL 33199, USA

Received 31 May 2014; Revised 17 September 2014; Accepted 1 October 2014; Published 19 October 2014

Academic Editor: Vladas Pipiras

Copyright © 2014 Zhenmin Chen and Tieyong Hu. 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.


The purpose of the multidimension uniformity test is to check whether the underlying probability distribution of a multidimensional population differs from the multidimensional uniform distribution. The multidimensional uniformity test has applications in various fields such as biology, astronomy, and computer science. Such a test, however, has received less attention in the literature compared with the univariate case. A new test statistic for checking multidimensional uniformity is proposed in this paper. Some important properties of the proposed test statistic are discussed. As a special case, the bivariate statistic test is discussed in detail in this paper. The Monte Carlo simulation is used to compare the power of the newly proposed test with the distance-to-boundary test, which is a recently published statistical test for multidimensional uniformity. It has been shown that the test proposed in this paper is more powerful than the distance-to-boundary test in some cases.