On two‐sample tests for circular data based on spacing‐frequencies
Riccardo Gatto, S. Rao Jammalamadaka · Wiley series in probability and statistics · 2015
Ranks and tests based on them are not applicable in comparing two circular samples, whereas tests based on the counts or frequencies of one sample that fall in between the spacings of the other sample, called “spacing-frequencies,” are. These are analysed with respect to their invariance and maximality and illustrated, including the classical Mardia–Watson–Wheeler test. A new test that is analogous to Rao's one-sample spacings test is introduced and its exact null distribution and a saddle-point approximation discussed. A Monte Carlo power comparison of Mardia–Watson–Wheeler test, Dixon's test and Rao's two-sample spacing-frequencies test shows that if bimodality is suspected for one of the two samples, then Rao's and Dixon's spacing-frequencies tests have superior power, compared to the familiar Wheeler–Watson test.