Too many skew normal distributions? The practitioner’s perspective

The paper tackles the issue of possible misspecification in fitting skew normal distributions to empirical data. It is shown, through numerical experiments, that it is easy to choose a distribution which is different from this which actually generated the sample, if the minimum distance criterion is used. It is suggested that, in case of similar values of distance measures obtained for different distributions, the choice should be made on the grounds of parameters’ interpretation rather than the goodness of fit. This is supported by empirical evidence of fitting different skew normal distributions to the estimated monthly inflation uncertainties for Belarus, Poland, Russia and Ukraine.