Beran’s tests of uniformity for discrete data (Michael Orrison, HMC)

Suppose you are given a data set that can be viewed as a nonnegative integer-valued function defined on a finite set. A natural question to ask is whether the data can be viewed as a sample from the uniform distribution on the set, in which case you might want to apply some sort of test of uniformity to the data. In this talk, I will share some work Anna Bargagliotti (Loyola Marymount University) and I have been doing to better understand a particular class of tests of uniformity first described in a 1968 paper written by R.J. Beran. Our approach uses tools from harmonic analysis on finite groups, and in this talk I will introduce those tools and then show how they can easily be used when working with discrete circular data.