Since about the turn of the millennium, the study of parametric families of probability distributions has received new, intense interest. The present work is an account of one approach which has generated a great deal of activity.

The distinctive feature of the construction to be discussed is to start from a symmetric density function and, by suitable modification of this, generate a set of non-symmetric distributions. The simplest effect of this process is represented by skewness in the distribution so obtained, and this explains why the prefix ‘skew’ recurs so often in this context. The focus of this construction is not, however, skewness as such, and we shall not discuss the quintessential nature of skewness and how to measure it. The target is in-stead to study flexible parametric families of continuous distributions for use in statistical work. A great deal of those in standard use are symmetric, when the sample space is unbounded. The aim here is to allow for possible departure from symmetry to produce more flexible and more realistic families of distributions.

The concentrated development of research in this area has attracted the interest of both scientists and practitioners, but often the variety of proposals and the existence of related but different formulations bewilders them, as we have been told by a number of colleagues in recent years. The main aim of this work is to provide a key to enter this theme.