Exact Asymptotic Goodness-of-Fit Testing For Discrete Circular Data, With Applications

We show that the full asymptotic null distribution for Watson’s 2N U statistic, modified for discrete data, can be computed simply and exactly by standard methods. Previous approximate quantiles for the uniform multinomial case are found to be accurate. More extensive quantiles are presented for this distribution, as well as for the beta-binomial distribution and for the distributions associated with “Benford’s Laws”. A simulation experiment compares the power of the modified 2N U test with that of Kuiper’s VN test. In addition, four illustrative empirical applications are provided. In addition, four illustrative empirical applications are provided to illustrate the usefulness of the 2N U test. (This paper supercedes EWP0607.)