Skewnesse

Skewnesse is a term used in theoretical discussions of asymmetry in geometry and statistics. It describes a measure of how far a distribution or shape is from central symmetry, serving as a multidimensional extension of the familiar concept of skewness. The term is not widely standardized and appears mainly in exploratory or speculative contexts, where researchers seek to quantify directional imbalance in data or forms.

Definition and computation: For a d-dimensional random vector X with mean μ, one can examine the projection of X onto a unit direction u. A directional skewnesse can be defined as Sk(u) = E[((X−μ)·u)^3] / E[((X−μ)·u)^2]^{3/2}, the third standardized moment of the projection. The overall skewnesse of the dataset may be summarized by the maximum value of |Sk(u)| over all directions u, with the sign indicating the sense of asymmetry along that axis. In shape analysis, skewnesse can be assessed by projecting boundary or contour points onto an axis and evaluating the asymmetry of the resulting profile.

Properties and usage: Skewnesse, like skewness, is sensitive to outliers and the scale of measurement. It can be influenced by sample size and may require robust estimation in practical applications. The concept is used in data exploration, pattern recognition, and morphometrics to identify axes with pronounced asymmetry or to compare groups with differing symmetry properties. Definitions and interpretations of skewnesse can vary between texts, reflecting its status as a nonstandard descriptor.

See also: skewness, asymmetry, multivariate statistics, morphometrics.