**6. Concluding Remarks**

The Mudholkar–Hutson skewing mechanism admits flexible extensions in both the univariate and multivariate cases. Stochastic representations of such extended models typically have corresponding likelihood functions that are somewhat complicated (for example Equations (4) and (9)). This is partly compensated for by the ease of simulation for such models using the representation in terms of latent variables ( the *Ui*'s and *Zi*'s in (2) or (8)). The data set analyzed in Section 5 illustrates the potential advantage of considering the extended bivariate Mudholkar-Hutson model, since the basic bivariate M-H model does not provide an acceptable fit to the "athletes" data. Needless to say, applying Occam's razor, it would always be desirable to consider the hierarchy of the five nested bivariate models that were considered in Section 5, in order to determine whether one of the simpler models might be adequate to describe a particular data set. Indeed there may be other special cases of the model (4), intermediate between (4) and (5) say, that might profitably be considered for some data sets. However, it should be remarked that selection of such sub-models for consideration should be done prior to inspecting the data. The addition of the GBMH model to the data analysts tool-kit should provide desirable flexibility for modeling data sets which exhibit behavior somewhat akin to, but not perfectly adapted to, more standard bivariate Cauchy models.

**Author Contributions:** All the authors contributed significantly to this research article.

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

**Acknowledgments:** The research of H. Varela and H.W. Gómez was supported by Grant SEMILLERO UA-2019 (Chile).

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