Van Zwet ordering for Fechner asymmetry

Abstract

There are several procedures to construct a skewed distribution. One of these procedures splits the value of a parameter of scale for the two halfs of a symmetric distribution. Fechner proposed this procedure in his famous book Kollektivmaßlehre (1897), p. 295ff.. A similar proposal comes from Fernandez et al. (1995). We consider the very general approach from Arellano-Valle et al. (2005) of splitting a scale parameter and show that this technique of generating skewed distributions incorporates a well-defined parameter of skewness. It is well-defined in the sense that the parameter of skewness is compatible with the orderingSkewness,skewness to the right,skewness ordering,measure of skewness