Directional (version 6.8)

Two sample location test for (hyper-)spherical data: Analysis of variance for (hyper-)spherical data

Description

Analysis of variance for (hyper-)spherical data.

Usage

spcauchy2test(y1, y2, B = 1)
pkbd2test(y1, y2, B = 1)

Value

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

statistic

The test statistic value.

parameter

The degree(s) of freedom of the test.

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

y1

A matrix with the data in Euclidean coordinates, i.e. unit vectors.

y2

A matrix with the data in Euclidean coordinates, i.e. unit vectors.

B

The number of bootstraps to perform.

Author

Michail Tsagris.

R implementation and documentation: Michail Tsagris .

Details

A log-likelihood ratio based test for the equality of two location parameters, assuming that the data in each group follow the spherical Cauchy of the Poisson-kernel based distribution. Bootstrap is also offered.

References

Kato S. and McCullagh P. (2020). Some properties of a Cauchy family on the sphere derived from the Mobius transformations. Bernoulli, 26(4): 3224--3248.

Golzy M. and Markatou M. (2020). Poisson kernel-based clustering on the sphere: convergence properties, identifiability, and a method of sampling. Journal of Computational and Graphical Statistics, 29(4): 758--770.

Tsagris M. (2024). Directional data analysis using the spherical Cauchy and the Poisson-kernel based distribution. https://arxiv.org/pdf/2409.03292

See Also

hcf.boot, hcfboot, hclr.circaov

Examples

mu <- rvmf(2, rnorm(5), 3)
y1 <- rspcauchy(60, mu[1, ], 0.4)
y2 <- rspcauchy(30, mu[2, ], 0.8)
spcauchy2test(y1, y2)