Weighted Goodness-of-fit Test for Circular Data

Weighted version of the Rayleigh test (or V0-test) for uniformity against a distribution with a priori expected von Mises concentration.

Usage

weighted_rayleigh(x, mu = NULL, w = NULL, axial = TRUE, quiet = FALSE)

Arguments

x

numeric vector. Values in degrees

mu

The a priori expected direction (in degrees) for the alternative hypothesis.

w

numeric vector weights of length length(x). If NULL, the non-weighted Rayleigh test is performed.

axial

logical. Whether the data are axial, i.e. \(\pi\)-periodical (TRUE, the default) or directional, i.e. \(2 \pi\)-periodical (FALSE).

quiet

logical. Prints the test's decision.

Value

a list with the components:

R or C

mean resultant length or the dispersion (if mu is specified). Small values of R (large values of C) will reject uniformity. Negative values of C indicate that vectors point in opposite directions (also lead to rejection).

statistic

Test statistic

p.value

significance level of the test statistic

Details

The Null hypothesis is uniformity (randomness). The alternative is a distribution with a (specified) mean direction (mu). If statistic >= p.value, the null hypothesis of randomness is rejected and angles derive from a distribution with a (or the specified) mean direction.

See also

rayleigh_test()

Examples

# Load data
data("cpm_models")
data(san_andreas)
PoR <- equivalent_rotation(subset(cpm_models, model == "NNR-MORVEL56"), "na", "pa")
sa.por <- PoR_shmax(san_andreas, PoR, "right")
data("iceland")
PoR.ice <- equivalent_rotation(subset(cpm_models, model == "NNR-MORVEL56"), "eu", "na")
ice.por <- PoR_shmax(iceland, PoR.ice, "out")
data("tibet")
PoR.tib <- equivalent_rotation(subset(cpm_models, model == "NNR-MORVEL56"), "eu", "in")
tibet.por <- PoR_shmax(tibet, PoR.tib, "in")

# GOF test:
weighted_rayleigh(tibet.por$azi.PoR, mu = 90, w = 1 / tibet$unc)
#> Reject Null Hypothesis
#> $C
#> [1] 0.5321474
#> 
#> $statistic
#> [1] 25.68679
#> 
#> $p.value
#> [1] 2.004315e-143
#> 
weighted_rayleigh(ice.por$azi.PoR, mu = 0, w = 1 / iceland$unc)
#> Reject Null Hypothesis
#> $C
#> [1] 0.3728874
#> 
#> $statistic
#> [1] 11.67322
#> 
#> $p.value
#> [1] 1.826316e-32
#> 
weighted_rayleigh(sa.por$azi.PoR, mu = 135, w = 1 / san_andreas$unc)
#> Reject Null Hypothesis
#> $C
#> [1] 0.8042366
#> 
#> $statistic
#> [1] 38.16524
#> 
#> $p.value
#> [1] 3.589557e-315
#>