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"))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.
Validation status
This retained legacy interface is experimental. Its full numerical and
statistical contract has not been independently verified across supported
inputs. See riem-method-contracts and the installed contract
table for method-specific assumptions, restrictions, and evidence scope.
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 and Sons, Inc., Hoboken, NJ, USA. ISBN 978-0-470-31697-9 978-0-471-95333-3.
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")
#>
#> Rayleigh Test of Uniformity on Sphere
#>
#> data: myobj
#> statistic = 4.8459, p-value = 0.435
#> alternative hypothesis: data is not uniformly distributed on 4-sphere.
#>
sphere.utest(myobj, method="rayleighm")
#>
#> Modified Rayleigh Test of Uniformity on Sphere
#>
#> data: myobj
#> statistic = 4.8385, p-value = 0.4359
#> alternative hypothesis: data is not uniformly distributed on 4-sphere.
#>