sphere.utest: Test of Uniformity on Sphere

In Riemann: Learning with Data on Riemannian Manifolds

Test of Uniformity on Sphere

Description

Given N observations \lbrace X_1, X_2, \ldots, X_M \brace on \mathcal{S}^{p-1}, it tests whether the data is distributed uniformly on the sphere.

Usage

sphere.utest(spobj, method = c("Rayleigh", "RayleighM"))

Arguments

spobj	a S3 "riemdata" class for N Sphere-valued data.
method	(case-insensitive) name of the test method containing "Rayleigh" original Rayleigh statistic. "RayleighM" modified Rayleigh statistic with better order of error.

Value

a (list) object of S3 class htest containing:

statistic

a test statistic.

p.value

p-value under H_0.

alternative

alternative hypothesis.

method

name of the test.

data.name

name(s) of provided sample data.

References

\insertRef

chikuse_statistics_2003Riemann

\insertRef

mardia_directional_1999Riemann

See Also

wrap.sphere

Examples

#-------------------------------------------------------------------
#   Compare Rayleigh's original and modified versions of the test
#-------------------------------------------------------------------
#  Data Generation
myobj = sphere.runif(n=100, p=5, type="riemdata")

#  Compare 2 versions : Original vs Modified Rayleigh
sphere.utest(myobj, method="rayleigh")
sphere.utest(myobj, method="rayleighm")

Riemann documentation built on March 25, 2026, 9:06 a.m.