A measure of asymmetry

作者：Patil P N; Patil P P; Bagkavos D^*

来源：Statistical Papers, 2012, 53(4): 971-985.

DOI：10.1007/s00362-011-0401-6

• Asymmetry measure
• Correlation
• Nonparametric
• Skewness

It is a general practice to make assertions about the symmetry or asymmetry of a probability density function based on the coefficients of skewness. Since most of the coefficients of skewness are designed to be zero for a symmetric density, they overall do provide an indication of symmetry. However, skewness is primarily influenced by the tail behavior of a density function, and the skewness coefficients are designed to capture this behavior. Thus they do not calibrate asymmetry in the density curves. We provide a necessary condition for a probability density function to be symmetric and use that to measure asymmetry in a continuous density curve on the scale of -1 to 1. We show through examples that the proposed measure does an admirable job of capturing the visual impression of asymmetry of a continuous density function.

• 出版日期2012-11