Second Central Momentum

Measures the skewness (a measure of the asymmetry of the probability distribution) and the kurtosis (measure of the "tailedness" of the probability distribution). Standardized versions are the skewness and kurtosis normalized by the mean resultant length, Mardia 1972).

Usage

second_central_moment(x, w = NULL, axial = TRUE, na.rm = FALSE)

Arguments

x

numeric vector. Values in degrees.

w

(optional) Weights. A vector of positive numbers and of the same length as x.

axial

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

na.rm

logical value indicating whether NA values in x should be stripped before the computation proceeds.

Value

list containing

skewness

second central sine momentum, i.e. the skewness

std_skewness

standardized skewness

kurtosis

second central cosine momentum, i.e. the kurtosis

std_kurtosis

standardized kurtosis

Details

Negative values of skewness indicate skewed data in counterclockwise direction.

Large kurtosis values indicate tailed, values close to 0 indicate packed data.

Examples

data("nuvel1")
PoR <- subset(nuvel1, nuvel1$plate.rot == "na")
sa.por <- PoR_shmax(san_andreas, PoR, "right")
second_central_moment(sa.por$azi.PoR)
#> $skewness
#> [1] -0.04045237
#> 
#> $std_skewness
#> [1] -0.4009978
#> 
#> $kurtosis
#> [1] 0.4903282
#> 
#> $std_kurtosis
#> [1] 2.42505
#> 
second_central_moment(sa.por$azi.PoR, w = 1 / san_andreas$unc)
#> $skewness
#> [1] -0.04566169
#> 
#> $std_skewness
#> [1] -0.4526369
#> 
#> $kurtosis
#> [1] 0.4451044
#> 
#> $std_kurtosis
#> [1] 1.462039
#>