# skewness: Skewness In e1071: Misc Functions of the Department of Statistics, Probability Theory Group (Formerly: E1071), TU Wien

 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 = ∑_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)
```

e1071 documentation built on June 7, 2022, 5:07 p.m.