Hypothesis test for von Mises-Fisher distribution over Kent distribution {Directional}

Hypothesis test for von Mises-Fisher distribution over Kent distribution

Description

The null hypothesis is whether a von Mises-Fisher distribution fits the data well, where the altenrative is that Kent distribution is more suitable.

Usage

fishkent(x, B = 999)

Arguments

x

A numeric matrix containing the data as unit vectors in Euclidean coordinates.

B

The number of bootstrap re-samples. By default is set to 999. If it is equal to 1, no bootstrap is performed and the p-value is obtained throught the asymptotic distribution.

Details

Essentially it is a test of rotational symmetry, whether Kent's ovalness parameter (beta) is equal to zero. This works for spherical data only.

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].

References

Rivest L. P. (1986). Modified Kent's statistics for testing goodness of fit for the Fisher distribution in small concentrated samples. Statistics & Probability Letters, 4(1): 1–4.

See Also

iagesag, pc.test, vmf.mle, kent.mle

Examples

x <- rvmf(100, rnorm(3), 15)
fishkent(x)
fishkent(x, B = 1)
iagesag(x)