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).
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 inx
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
#>