Score test of the Fisher against the Kent distribution

Usage

fisher_kent_test(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

\(T = n (\kappa/2)^2 I_1/2(\kappa) / I_5/2(\kappa) r_2^2\) is asymptotically chi-square with 2 degrees of freedom (Kent, 1982, eq. 5.5), with the maximum-likelihood \(\kappa\) of the Fisher distribution (Kent's Theorem 5.1) and \(r_2\) the difference of the two eigenvalues of the second moments of the data in the tangent plane of the mean direction.

Large \(T\) indicates elliptical (Kent) rather than circular (Fisher) contours.

Note

FLE (sec. 5.4.6) computes the statistic with the concentration of the fitted Kent distribution, which gives a larger value; this follows Kent's theorem.

References

Kent, J.T. (1982). The Fisher-Bingham distribution on the sphere. Journal of the Royal Statistical Society B 44, 71-80.

Examples

#' set.seed(20250411)
x <- rvmf(100)
fisher_kent_test(x)
#> 
#> 	Fisher vs Kent
#> 
#> statistic = 0.12966, df = 2, p-value = 0.9372
#> critical value (95% confidence level) = 5.9915
#> null hypothesis rejected at the 95% confidence level: no
#> further statistics:
#>      kappa         r2 
#> 5.66200190 0.00954967 
#> source: Kent (1982), eq. 5.5 
#>