Geary's characterization of the normal distribution asserts that if $n \geqslant 2$ i.i.d. observations come from some distribution on the line, then the sample mean and variance are independent if and only if the observations are normally distributed. A similar characterization is established here for the uniform distribution on the circle. Given a sample of $n \geqslant 2$ i.i.d. random angles from a distribution defined by a density on the circle satisfying some mild regularity conditions, the sample mean direction and resultant length are independent if and only if the angles come from the uniform distribution.
Publié le : 1979-07-14
Classification:
Directional data,
uniform distribution,
independence of mean direction,
resultant length,
62E10
@article{1176344737,
author = {Kent, J. T. and Mardia, K. V. and Rao, J. S.},
title = {A Characterization of the Uniform Distribution on the Circle},
journal = {Ann. Statist.},
volume = {7},
number = {1},
year = {1979},
pages = { 882-889},
language = {en},
url = {http://dml.mathdoc.fr/item/1176344737}
}
Kent, J. T.; Mardia, K. V.; Rao, J. S. A Characterization of the Uniform Distribution on the Circle. Ann. Statist., Tome 7 (1979) no. 1, pp. 882-889. http://gdmltest.u-ga.fr/item/1176344737/