Hodges-Ajne Test

Hodges-Ajne test of uniformity on the circle

Usage

hodges_ajne_test(x, alpha = 0.05, axial = TRUE)

Arguments

x

numeric vector. Values in degrees

alpha

Significance level of the test ranging between 0 and 1.

axial

logical. Whether the data are axial, i.e. \(\pi\)-periodical (TRUE, the default) or directional, i.e. \(2 \pi\)-periodical (FALSE). In case of axial data, the angles will be doubled for the test.

Value

A list with class "htest" containing the following components:

statistic

the value of the m statistic

parameter

the number of data

p.value

the p-value for the test

alternative

a character string describing the alternative hypothesis.

method

a character string indicating what type of test was performed.

data.name

a character string giving the name(s) of the data.

Details

The statistic \(m\) is the smallest number of angles in a half-circle. Its exact distribution is $$P(m \le t) = 2^{(1 - n)} (n - 2t) C(n, t)$$ for \(t < n / 3\) (Mardia and Jupp, 2000, sec. 6.3.4), which gives the p-value (1 above \(n / 3\)). Small \(m\) indicates a preferred direction.

See also

Other One-Sample-Tests: kuiper_test(), norm_chisq(), rao_spacing_test(), rayleigh-test, watson_test(), weighted-rayleigh-test

Examples

hodges_ajne_test(rvm(100, mean = 0, kappa = 10))
#> 
#> 	Hodges-Ajne test of uniformity
#> 
#> data:  rvm(100, mean = 0, kappa = 10)
#> m = 1, n = 100, p-value < 2.2e-16
#> alternative hypothesis: unimodal distribution
#> 

# San Andreas Fault Data:
data(san_andreas)
data("nuvel1")
PoR <- subset(nuvel1, nuvel1$plate.rot == "na")
sa.por <- PoR_shmax(san_andreas, PoR, "right")
hodges_ajne_test(sa.por$azi.PoR, alpha = .05)
#> 
#> 	Hodges-Ajne test of uniformity
#> 
#> data:  sa.por$azi.PoR
#> m = 76, n = 1126, p-value < 2.2e-16
#> alternative hypothesis: unimodal distribution
#>