need for another measure of asymmetry that has this property: such a measure was introduced in 2000. It is called distance skewness and denoted by dSkew. If X is a random variable taking values in the d-dimensional Euclidean space, X has finite expectation, X is an independent identically distributed copy of X, and denotes the norm in the Euclidean space, then a simple measure of asymmetry with respect to location parameter θ is and dSkew(X) := 0 for X = θ (with probability 1). Distance skewness is always between 0 and 1, equals 0 if and only if X is diagonally symmetric with respect to θ (X and 2θ−X have the same probability distribution) and equals 1 if and only if X is a constant c'' () with probability one. Thus there is a simple consistent statistical test of diagonal symmetry based on the sample distance skewness: Medcouple The medcouple is a scale-invariant robust measure of skewness, with a breakdown point of 25%. It is the median of the values of the kernel function taken over all couples such that , where is the median of the sample . It can be seen as the median of all possible quantile skewness measures. See also Bragg peak Coskewness Kurtosis Shape parameters Skew normal distribution Skewness risk References Citations Sources Premaratne, G., Bera, A. K. (2001). Adjusting the Tests for Skewness and Kurtosis for Distributional Misspecifications. Working Paper Number 01-0116, University of Illinois. Forthcoming in Comm in Statistics, Simulation and Computation. 2016 1-15 Premaratne, G., Bera, A. K. (2000). Modeling Asymmetry and Excess Kurtosis in Stock Return Data. Office of Research Working Paper Number 00-0123, University of Illinois. Skewness Measures for the Weibull Distribution External links An Asymmetry Coefficient for Multivariate Distributions by Michel Petitjean On More Robust Estimation of Skewness and Kurtosis Comparison of skew estimators by Kim and White. Closed-skew Distributions — Simulation, Inversion and Parameter Estimation Moment (mathematics) Statistical deviation and dispersion