Pairwise Difference Representations of Moments: Gini and Generalized Lagrange identities
矩的成对差分表示:基尼型与广义拉格朗日恒等式
We provide pairwise-difference (Gini-type) representations of higher-order central moments for both general random variables and empirical moments. Such representations do not require a measure of location. For third and fourth moments, this yields pairwise-difference representations of skewness and kurtosis coefficients. We show that all central moments possess such representations, so no reference to the mean is needed for moments of any order. This is done by considering…