skew.misc {univOutl} | R Documentation |
Calculates some skewness measures.
Description
The function calculates some skewness measures for the input vector data.
Usage
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 |
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:
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:
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:
Similarly
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 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.
See Also
Examples
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)