univOutl (version 0.4)

skew.misc: 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 x

Value

A vector with the estimated measures of skewness.

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:

$$b = \frac{(Q_3 - Q_2) - (Q_2 - Q_1) }{Q_3 - Q_1} $$

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:

$$ g=\frac{1+b}{1-b} $$

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:

$$b_P = \frac{(P_{90} - P_{50}) - (P_{50} - P_{10}) }{P_{90} - P_{10}} $$

Similarly $$ g_P=\frac{1+b_P}{1-b_P} $$

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.

References

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

See Also

mc

Examples

# NOT RUN {
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)

# }