skewness function

Skewness

This function encodes different methods to calculate the skewness from a vector of observations.

skewness(x, na.rm = FALSE, method = c("moment", "fisher", "bickel"), M, ...)

Arguments

• x: numeric. Vector of observations.
• na.rm: logical. Should missing values be removed?
• method: character. Specifies the method of computation. These are either "moment", "fisher" or "bickel". The "moment" method is based on the definition of skewness for distributions; this form should be used when resampling (bootstrap or jackknife). The "fisher" method corresponds to the usual "unbiased" definition of sample variance, although in the case of skewness exact unbiasedness is not possible.
• M: numeric. (An estimate of) the mode of the observations x. Default value is shorth(x).
• ...: Additional arguments.

Returns

skewness returns a numeric value. An attribute reports the method used.

Examples

# = 0
x <- rnorm(1000)
skewness(x, method = "bickel", M = shorth(x))

# > 0 (left skewed case)
x <- rbeta(1000, 2, 5)
skewness(x, method = "bickel", M = betaMode(2, 5))

# < 0 (right skewed case)
x <- rbeta(1000, 7, 2)
skewness(x, method = "bickel", M = hsm(x, bw = 1/3))

References

• Bickel D.R. (2002). Robust estimators of the mode and skewness of continuous data. Computational Statistics and Data Analysis, 39 :153-163.
• Bickel D.R. et Fruehwirth R. (2006). On a Fast, Robust Estimator of the Mode: Comparisons to Other Robust Estimators with Applications. Computational Statistics and Data Analysis, 50 (12):3500-3530.

See Also

mlv for general mode estimation; shorth for the shorth estimate of the mode

Author(s)

Diethelm Wuertz and contributors for the original skewness function from package fBasics.