Signal distribution moments (mean, SD, skewness, kurtosis)

Computes the first four moments of a one-dimensional signal's amplitude distribution: the mean, the (population) standard deviation, the skewness, and the excess kurtosis. Skewness measures asymmetry (negative = a longer left tail); excess kurtosis measures tailedness relative to a Gaussian (0 = Gaussian, positive = heavier tails / more peaked). These are the standard shape descriptors used, for example, to flag EEG artifacts (high kurtosis) or characterize amplitude asymmetry. Definitions match scipy.stats.skew (biased) and scipy.stats.kurtosis (Fisher / excess, biased), with the population standard deviation (ddof = 0).

Usage

signalMoments(x)

Arguments

x

A numeric vector (the time series).

Value

A list with mean, sd (population), skewness, and kurtosis (excess).

References

Joanes, D.N., Gill, C.A. (1998). Comparing measures of sample skewness and kurtosis. The Statistician, 47(1), 183-189.

See also

sd

Examples

set.seed(1)
signalMoments(rnorm(1000))   # ~ 0 skewness, ~ 0 excess kurtosis for Gaussian
#> $mean
#> [1] -0.01164814
#> 
#> $sd
#> [1] 1.034398
#> 
#> $skewness
#> [1] -0.0191671
#> 
#> $kurtosis
#> [1] -0.001775465
#>