Abstract
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.
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Patil, P.N., Patil, P.P. & Bagkavos, D. A measure of asymmetry. Stat Papers 53, 971–985 (2012). https://doi.org/10.1007/s00362-011-0401-6
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DOI: https://doi.org/10.1007/s00362-011-0401-6