hodges_ajne_test: Hodges-Ajne Test

Description

Hodges-Ajne test of uniformity on the circle

Usage

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

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.

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.

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.

Examples

Run this code

hodges_ajne_test(rvm(100, mean = 0, kappa = 10))

# 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)