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On Tests of Uniformity for Randomly Distributed Arcs on a Circle
Author(s) -
Kokic P. N.
Publication year - 1987
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1987.tb00733.x
Subject(s) - clockwise , point (geometry) , mathematics , simple (philosophy) , power (physics) , vacancy defect , geometry , combinatorics , mathematical analysis , physics , condensed matter physics , quantum mechanics , philosophy , rotation (mathematics) , epistemology
Summary Let n points be independently distributed on a circle. Moving in a counter‐clockwise direction, place arcs of length a on the circle with the i th are starting at the i th point. We describe three simple tests of the hypothesis of uniformity based on vacancy, on number of spacings and on the length of the maximal spacing. The tests do not require knowledge of the random points. The asymptotic power of these tests is investigated, and it is shown that vacancy‐based tests perform best of the three.