A Simple Test for Uniformity of a Circular Distribution

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARY Consider a finite set of points, located on the circumference of a circle. Several tests have been proposed of the hypothesis that the points constitute a random sample from a uniform distribution. In this paper we study a test statistic defined as the maximal number of points that can be covered by some semicircle. Exact and asymptotic distributions under the null hypothesis, and under a certain alternative hypothesis, are given together with some tables. A related test statistic is studied briefly. An expression is obtained concerning most powerful invariant tests of the hypothesis of a uniform circular distribution.

Error-driven learning in statistical summary perception.

“…These angles were tested for uniformity using the Hodges-Ajne test, a non-parametric test of deviations from uniformity in circular data (Ajne, 1968; Zar, 1999). In the absence of a directional bias, the distribution of these angles should be circularly uniform around the centroid on average (in the range [−180°,180°]), where θ=0 was defined as pure rightward bias, and counterclockwise rotation is positive).…”

Analyzing and Modeling Data and Knowledge

“…As to clusters in time, Tango (1984) and others have distinguished between temporal clusters, which can be found, for instance, with infectious diseases, and cyclical clusters, which may be caused by a cyclical environmental factor. For the continuous circular scan statistic, corresponding results have been derived for its exact and asymptotic distributions (Ajne (1968), Rothman (1972), Cressie (1977a,b), Wallenstein, Weinberg and Gould (1989)). Scan statistics are defined as the maximum number of cases which can be observed in a window of given length which is scanned over the time interval in question.…”

A Goodness-Of-Fit Statistic for the Circle, with Some Comparisons

“…Two goodness-of-fit statistics have recently been suggested by Ajne (1968), for use with observations recorded as points on the circumference of a circle. Suppose that the random variable y is the arc length, measured from a suitably chosen origin, around the circumference of a circle whose total circumference is L; if the points record directions, North may he taken, say, as origin, and the positive direction clockwise.…”