Directional (version 6.1)

Hypothesis test for SIPC distribution over the SESPC distribution: Hypothesis test for SIPC distribution over the SESPC distribution

Description

The null hypothesis is whether an SIPC distribution fits the data well, where the altenrative is that SESPC distribution is more suitable.

Usage

pc.test(x, B = 1, tol = 1e-06)

Value

A vector including:

test

The value of the test statistic.

p-value or Bootstrap p-value

The p-value of the test.

Arguments

x

A numeric matrix with three columns 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.

tol

The tolerance to accept that the Newton-Raphson algorithm used in the IAG distribution has converged.

Author

Michail Tsagris.

R implementation and documentation: Michail Tsagris .

Details

Essentially it is a test of rotational symmetry, whether the two \(\theta\) parameters are equal to zero. This works for spherical data only.

References

Tsagris M. and Alzeley O. (2023). Circular and spherical projected Cauchy distributions. https://arxiv.org/pdf/2302.02468.pdf

See Also

iagesag, fishkent, sespc.mle

Examples

x <- rvmf(100, rnorm(3), 15)
iagesag(x)
pc.test(x)