sphere.utest {Riemann}

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

Chikuse Y (2003). Statistics on Special Manifolds, volume 174 of Lecture Notes in Statistics. Springer New York, New York, NY. ISBN 978-0-387-00160-9 978-0-387-21540-2.

Mardia KV, Jupp PE (eds.) (1999). Directional Statistics, Wiley Series in Probability and Statistics. John Wiley \& Sons, Inc., Hoboken, NJ, USA. ISBN 978-0-470-31697-9 978-0-471-95333-3.

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")