# skew.misc: Calculates some skewness measures. In univOutl: Detection of Univariate Outliers

## Description

The function calculates some skewness measures for the input vector data.

## Usage

 `1` ```skew.misc(x, weights=NULL) ```

## Arguments

 `x` Input vector containing data for which skewness will be calculated. `weights` Optional vector with eventual non-negative weights associated to the units in `x`

## Details

This function calculates Pearson's skewness coefficient, the MedCouple measure of skewness and the non-parametric Bowley's measure of symmetry. The Bowley's skewness measure uses quartiles:

b = ((Q3 - Q2) - (Q2 - Q1))/(Q3 - Q1)

It ranges between -1 and +1, where positive (negative) values denote right (left) skewness. A value equal to 0 indicates symmetry. A crude measure of skewness can be obtained with a monotonic increasing function of b:

g = (1+b)/(1-b)

It ranges from 0 to Inf, g=1 indicates symmetry.

A measure of skewness similar to the Bowley's one is achieved by replacing Q3 and Q1 with respectively P90 and P10 percentiles:

b_P = ((P90 - P50) - (P50 - p10))/(P90 - P10)

Similarly

g_P = (1+b_P)/(1-b_P)

For major details see Kotz at al. (2006, vol. 12, pp. 7771-7772).

The medCouple measure of skewness, M, ranges from -1 to +1 and is equal to 0 in case of symmetry, while M>0 indicates positive skewness. For major details see `mc`.

Note that eventual weights, passed through the argument `weights`, are used ONLY in the calculation of the Bowley's type measures.

## Value

A vector with the estimated measures of skewness.

## Author(s)

Marcello D'Orazio mdo.statmatch@gmail.com

## References

Kotz S. et al. (2006) Encyclopedia of Statistical Sciences, Volume 12. John Wiley and Sons.

`mc`
 ```1 2 3 4 5 6 7 8 9``` ```set.seed(112233) y <- rnorm(n = 30, mean = 50, sd = 10) y[20] <- 100 skew.misc(x = y, weights=NULL) # use weights ww <- runif(n = 30, min = 1, max = 10) skew.misc(x = y, weights=ww) ```