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It checkes whether the data are uniformly distributed on the sphere or hypersphere.
rayleigh(x, modif = TRUE, B = 999)A matrix containing the data, unit vectors.
If modif is TRUE, the modification as suggested by Jupp (2001) is used.
If B is greater than 1, bootstap calibation os performed. If it is equal to 1, classical theory is used.
A vector including:
The value of the test statistic.
The (bootstrap) p-value of the test.
The Rayleigh test of uniformity is not the best, when there are two antipodal mean directions. In this case it will fail. It is good to test whether there is one mean direction or not. To put it differently, it tests whether the concentration parameter of the Fisher distribution is zero or not.
Mardia, K. V. and Jupp, P. E. (2000). Directional statistics. Chicester: John Wiley & Sons.
Jupp, P. E. (2001). Modifications of the rayleigh and bingham tests for uniformity of directions. Journal of Multivariate Analysis, 77(2):1-20.
Rayleigh, L. (1919). On the problem of random vibrations, and of random flights in one, two, or three dimensions. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 37(220):321-347.
# NOT RUN {
x <- rvmf(100, rnorm(5), 1) ## Fisher distribution with low concentration
rayleigh(x)
# }
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