**4. Conclusions**

In this paper two main objectives are achieved: on the one hand, the given examples show that the skewness function orders the mesh in good accordance with the intuitive conception of skewness. Moreover, these examples show that the skewness of a distribution obtained from certain parametric families can be controlled by reference to their parameters.

As we show, the function *νF* (*z*) facilitates the description of a random variable by means of a probability distribution, by making any skewness in the model easily observable and should be undertaken to examine the use of these properties in data fitting.

In practice, much can be learned from this model, but there remains the risk that it may be wrongly specified in real applications. Thus, in practice we must be willing to assume that the underlying distribution has a unique mode and belongs to a uniparametric family of distributions.

In many practical situations, the maximum skewness index coincides with the well known *γM* (*F*), but this second index only takes into account the difference of probability weights at each side of the mode, while the first takes a value from the point where this difference is maximum. Moreover, the aggregate skewness function gives more accurate information about how the probability weight is distributed along both sides of the mode. Accordingly, the condition *F* ≥*ν G* provides highly valuable information.

**Author Contributions:** All authors have contributed equally to this paper.

**Funding:** This research received no external funding.

**Acknowledgments:** This research was partially funded by MINECO (Spain) gran<sup>t</sup> number EC02017–85577–P. The authors are grateful for helpful suggestions made by two reviewers.

**Conflicts of Interest:** The authors declare no conflict of interest.
