Description Usage Arguments Details Value Author(s) References See Also Examples

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

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`x` |
Input vector containing data for which skewness will be calculated. |

`weights` |
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)*

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.

A vector with the estimated measures of skewness.

Marcello D'Orazio mdo.statmatch@gmail.com

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

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