Skewnes by splitting the scale parameter

There are several possibilities to introduce skewness into a symmetric distribution. One ofthese procedures applies two di®erent parameters of scale { with possibly di®erent weights {to the positive and the negative part of a symmetric density. Within this work we show thatthis technique incorporates a well-de¯ned parameter of skewness, i.e. that the generateddistributions are skewed to the right (left) if the parameter of skewness takes values less(greater) than one. Secondly, we prove that the skewness parameter is compatible withthe skewness ordering of van Zwet (1964) which is the strongest ordering in the hierarchyof orderings discussed by Oja (1981). Hence, the generated (skewed) distributions can beordered by the skewness parameter.