SOME TESTS BASED ON ARC-LENGTHS FOR THE CIRCLE

Abstract

SUMMARY. Tests for circular populations based on sample arc-lengths, i.e., distances between consecutive observations on the circumference, are considered for the following two problems (i) testing goodness of fit, and (ii) testing Whether two circular populations are identical. For problem (i) if Dx, ..., D? are the sample arc-lengths made by a random sample of size n, we discuss in Sections 1 and 2 some tests based symmetrically on {?>?} and comment on their asymptotic efficiencies. Section 3 deals with comparison of two circular populations for which we suggest a test called the F-test which is shown to be asymptotically superior to the standard Run test for the circle (see for instance David and Barton (1962)).