Rayleigh's test of uniformity {Directional}

Rayleigh's test of uniformity

Description

It checkes whether the data are uniformly distributed on the circle or the (hyper-)sphere.

Usage

rayleigh(x, modif = TRUE, B = 999)

Arguments

x

A matrix containing the data, unit vectors.

modif

If modif is TRUE, the modification as suggested by Jupp (2001) is used.

B

If B is greater than 1, bootstap calibation os performed. If it is equal to 1, classical theory is used.

Details

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.

Value

This is an "htest"class object. Thus it returns a list including:

statistic

The test statistic value.

parameter

The degrees of freedom of the test. If bootstrap was employed this is "NA".

p.value

The p-value of the test.

alternative

A character with the alternative hypothesis.

method

A character with the test used.

data.name

A character vector with two elements.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail] and Giorgos Athineou <[e-mail]>.

References

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.

See Also

ptest, kuiper, iagesag

Examples

x <- rvmf(100, rnorm(5), 1)  ## Fisher distribution with low concentration
rayleigh(x)