Kuiper Test of Circular Uniformity — kuiper

Kuiper test for circular random distribution.

Usage

kuiper_test(x, alpha = 0, axial = TRUE)

Arguments

x: numeric vector containing the circular data which are expressed in degrees
alpha: Significance level of the test. Valid levels are 0.01, 0.05, and 0.1. This argument may be omitted (NULL, the default), in which case, a range for the p-value will be returned.
axial: logical. Whether the data are axial, i.e. \(\pi\)-periodical (TRUE, the default) or circular, i.e. \(2 \pi\)-periodical (FALSE).

Value

list containing the test statistic statistic and the significance level p.value.

Details

Kuiper's test statistic is a rotation-invariant Kolmogorov-type test statistic. The critical values of a modified Kuiper's test statistic are used according to the tabulation given in Stephens (1970).

If statistic > p.value, the null hypothesis is rejected. If not, randomness (uniform distribution) cannot be excluded.

Examples

# Example data from Mardia and Jupp (2001), pp. 93
pidgeon_homing <- c(55, 60, 65, 95, 100, 110, 260, 275, 285, 295)
kuiper_test(pidgeon_homing, alpha = .05)
#> Reject Null Hypothesis
#> $statistic
#> [1] 2.262115
#> 
#> $p.value
#> [1] 1.747
#> 

# San Andreas Fault Data:
data(san_andreas)
data("nuvel1")
PoR <- subset(nuvel1, nuvel1$plate.rot == "na")
sa.por <- PoR_shmax(san_andreas, PoR, "right")
kuiper_test(sa.por$azi.PoR, alpha = .05)
#> Reject Null Hypothesis
#> $statistic
#> [1] 16.36159
#> 
#> $p.value
#> [1] 1.747
#>