The null hypothesis is whether an SIPC distribution fits the data well, where the altenrative is that SESPC distribution is more suitable.
pc.test(x, B = 1, tol = 1e-06)This is an "htest"class object. Thus it returns a list including:
The test statistic value.
The degrees of freedom of the test. If bootstrap was employed this is "NA".
The p-value of the test.
A character with the alternative hypothesis.
A character with the test used.
A character vector with two elements.
A numeric matrix with three columns containing the data as unit vectors in Euclidean coordinates.
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.
The tolerance to accept that the Newton-Raphson algorithm used in the IAG distribution has converged.
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.
Essentially it is a test of rotational symmetry, whether the two \(\theta\) parameters are equal to zero. This works for spherical data only.
Tsagris M. and Alzeley O. (2023). Circular and spherical projected Cauchy distributions: A Novel Framework for Circular and Directional Data Modeling. https://arxiv.org/pdf/2302.02468.pdf
iagesag, fishkent, sespc.mle
x <- rvmf(100, rnorm(3), 15)
iagesag(x)
pc.test(x)
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