spcauchy2test: Two sample location test for (hyper-)spherical data

In Directional: A Collection of Functions for Directional Data Analysis

Two sample location test for (hyper-)spherical data

Description

Two sample location test for (hyper-)spherical data.

Usage

spcauchy2test(y1, y2, B = 1)
pkbd2test(y1, y2, B = 1)
sp2(y1, y2, tol = 1e-6)
pk2(y1, y2, tol = 1e-6)

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.
tol	The tolerance value at which to terminate the iterations.

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.

The functions sp2() and pk2() estimate the common location of the two groups assuming unequal concentration parameters. These functions are used the compute the log-likelihood under the null hypothesis.

Value

The result of the spcauchy2test() and pkbd2test() functions 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.

The result of the sp2() and pk2() function is a list including:

mu	The common location parameter, for both samples, under the null hypothesis.
rho1	The concentration parameter of the first group, asusming a common location parameter.
rho2	The concentration parameter of the second group, asusming a common location parameter.
loglik	The log-likelihood of the whole sample, asusming a common location parameter.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail].

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. and Papastamoulis P. (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)

Directional documentation built on Oct. 30, 2024, 9:15 a.m.