Directional (version 7.0)

Hypothesis test for von Mises-Fisher distribution over Kent distribution: 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)

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.

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.

Author

Michail Tsagris.

R implementation and documentation: Michail Tsagris .

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.

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)