2017/10/10 by Azzalini, Adelchi, Regoli, Giuliana
#60E99 #62E15 #62H99 #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.1710.03494
In the context of modulated-symmetry distributions, there exist various forms of skew-elliptical families. We present yet another one, but with an unusual feature: the modulation factor of the baseline elliptical density is represented by a distribution function with an argument which is not an odd function, as it occurs instead with the overwhelming majority of similar formulations, not only with other skew-elliptical families. The proposal is obtained by going back to the use of Lemma~1 of Azzalini and Capitanio (1999), which can be seen as the general frame for a vast number of existing formulations, and use it on a different route. The broader target is to show that this `mother lemma' can still generate novel progeny.