e1071 (version 1.7-6)

# skewness: Skewness

## Description

Computes the skewness.

## Usage

skewness(x, na.rm = FALSE, type = 3)

## Arguments

x

a numeric vector containing the values whose skewness is to be computed.

na.rm

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

type

an integer between 1 and 3 selecting one of the algorithms for computing skewness detailed below.

## Value

The estimated skewness of x.

## Details

If x contains missings and these are not removed, the skewness is NA.

Otherwise, write $$x_i$$ for the non-missing elements of x, $$n$$ for their number, $$\mu$$ for their mean, $$s$$ for their standard deviation, and $$m_r = \sum_i (x_i - \mu)^r / n$$ for the sample moments of order $$r$$.

Joanes and Gill (1998) discuss three methods for estimating skewness:

Type 1:

$$g_1 = m_3 / m_2^{3/2}$$. This is the typical definition used in many older textbooks.

Type 2:

$$G_1 = g_1 \sqrt{n(n-1)} / (n-2)$$. Used in SAS and SPSS.

Type 3:

$$b_1 = m_3 / s^3 = g_1 ((n-1)/n)^{3/2}$$. Used in MINITAB and BMDP.

All three skewness measures are unbiased under normality.

## References

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

## Examples

Run this code
# NOT RUN {
x <- rnorm(100)
skewness(x)
# }


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