# anderson.darling.test: Skewness In burrm/lolcat: Miscellaneous Useful Functions

 skewness R Documentation

## 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.

### 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.

### Value

The estimated skewness of x.

### References

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

### Examples

x <- rnorm(100)
skewness(x)


burrm/lolcat documentation built on Sept. 15, 2023, 11:35 a.m.