Measures of uniformity in experimental designs: A selective overview

ABSTRACT

Discrepancies are measures which are defined as the deviation between the empirical and the theoretical uniform distribution. In this way, discrepancy is a measure of uniformity which provides a way of construction a special kind of space filling designs, namely uniform designs. Several discrepancies have been proposed in recent literature. A brief, selective review of these measures including some construction algorithms are given in this paper. Furthermore, a critical discussion along with some comparisons is provided, as well.

Keywords:

• Discrepancy measures
• Uniformity
• Uniform designs
• Construction algorithms

MATHEMATICS SUBJECT CLASSIFICATION:

• 62K15

Acknowledgments

The authors would like to thank the Editor, an Associate Editor, and two Referees for their valuable comments and suggestions that led to improve the quality of presentation of the paper.

Funding

Zhou's research was partially supported by National Natural Science Foundation of China (11471229) and Fundamental Research Funds for the Central Universities (2013SCU04A43). Drosou's research was financially supported by a scholarship awarded by Captain Fanourakis Foundation and State Scholarships Foundation.