Groeneveld-Meeden's coefficient of skewness

Groeneven-Meeden's coefficient of skewness is a family of measures of skewness proposed by professors Richard A. Groeneveld and Glen Meeden in 1984. It's a generalization of the Bowley's coefficient of skewness. Its general formula is the following:

where $P_p$ and $P_{(1-p)}$ are the percentiles of rank , with $0<p<1/2$.

The interpretation of the coefficient is as follows:

• when $A_G>0$, the distribution is right-skewed;
• when $A_G<0$, the distribution is left-skewed.

The Bowley's coefficient of skewness is a special case of the Groeneven-Meeden's coefficient,  when the percentiles involved are $P_{25}$ and $P_{75}$, that is to say, the first and third quartiles respectively.