Rayleigh test of uniformity against a unimodal alternative

Rayleigh test of uniformity against a unimodal alternative

Usage

rayleigh_test3(x, level = 0.95)

Source

modified after the python package apsg (v.2.0.6) by O. Lexa

Arguments

x

Object of class spherical

level

numeric. Confidence level (\(1-\alpha\)). Default is 0.95

Value

object of class "Test"

Details

The statistic is \(S = p n \bar{R}^2\) for \(n\) unit vectors in \(p\) dimensions, asymptotically chi-square with \(p\) degrees of freedom; the p-value is that of the modified statistic \(S^* = (1 - 1/(2n)) S + S^2 / (2n(p + 2))\), which has error \(O(1/n^2)\) (MJ eq. 10.4.4-10.4.6, eq. 6.3.3 for the circle; FLE sec. 5.3.1(i)). The test is not consistent against axial alternatives.

See also

Other tests: bingham_test(), fisher_ftest(), fisher_goodness_of_fit(), fisher_kent_test(), watson_symmetry_test(), wellner()

Examples

rayleigh_test3(example_lines)
#> 
#> 	Rayleigh Test
#> 
#> statistic = 1954991, df = 3, p-value < 2.2e-16
#> critical value (95% confidence level) = 7.8147
#> null hypothesis rejected at the 95% confidence level: yes
#> further statistics:
#>            R         Rbar     modified 
#> 7.398632e+03 8.807895e+01 4.551932e+09 
#> source: Mardia & Jupp (2000), eq. 10.4.4-10.4.6 
#>