modeest (version 2.1)

skewness: Skewness

Description

The skewness.default function from package fBasics is completed in order to implement Bickel's measure of skewness, based on the mode of the distribution considered.

Usage

skewness(x, 
         …)
  # S3 method for default
skewness(x, 
         na.rm = FALSE, 
         method = c("moment", "fisher", "bickel"), 
         M = shorth(x), 
         …)

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).

…

arguments to be passed.

Value

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

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

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

Examples

# NOT RUN {
## Skewness = 0
x <- rnorm(1000)
skewness(x, method = "bickel", M = shorth(x))

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

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