The function calculates some skewness measures for the input vector data.
Input vector containing data for which skewness will be calculated.
Optional vector with eventual non-negative weights associated to the units in
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)
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
Note that eventual weights, passed through the argument
weights, are used ONLY in the calculation of the Bowley's type measures.
A vector with the estimated measures of skewness.
Marcello D'Orazio email@example.com
Kotz S. et al. (2006) Encyclopedia of Statistical Sciences, Volume 12. John Wiley and Sons.
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