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Abstract:
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If f is a density function that is symmetric about 0 and G is the distribution function of a distribution that is symmetric about 0, then 2f(x)G(x) is a density function. Such distributions are called skew-symmetric distributions. Properties of moments of these distributions, especially skew, as they relate to f are discussed. In particular, even moments are independent of the choice of G, and the first moment always falls between 0 and the mean of folded distribution 2f(x) for x>0. Such results are extended to the parametric family, 2f(x)G(dx) for real d. It is shown, for example, that odd moments are increasing functions of d, but there is no general-order relations skew as defined by the central third moment.
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