Asymmetry and Gradient Asymmetry Functions: Density‐Based Skewness and Kurtosis

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Skewness-Invariant Measures of Kurtosis (2011, background): “A density-based “asymmetry function” (parallel to extended Bowley skewness in the quantile-based case) is γ (p) = xR(p) − 2x0 + xL(p) xR(p) − xL(p) (O’Hagan 1994, section 2.6; Avérous, Fougères, and Meste 1996; Boshnakov 2007; Critchley and Jones 2008).”
On Families of Distributions with Shape Parameters (2015, unknown): “(These distributions can be ‘log-symmetric’, a meaningful alternative to ordinary symmetry, along with ‘R-symmetry’, Mudholkar & Wang, 2007, on R + ; see Jones, 2008.)”