On a transform for modeling skewness

Abstract

In many applications, data exhibit skewness and in this paper we present a new family of density functions modeling skewness based on a transformation, analogous to those of location and scale. Here we note that location will always refer to mode. Hence, in order to model data to include shape, we need only to find a family of densities exhibiting a variety of shapes, since we can obtain the other three properties via the transformations. The chosen class of densities with the variety of shape is, we argue, the simplest available. Illustrations including regression and time series models are given.