Characterizations of the Generalized Beta-generated family of distributions.

Several characterizations of Generalized Beta-generated family of distributions, introduced by Alexander et al. (2012), are presented, giving special emphasis to the Kumaraswamy skew-normal distribution and the Beta skew-normal distribution, special cases of this family. These characterizations are based on: (i) a simple relationship between two truncated moments; (ii) the hazard function; (iii) a single function of the random variable; (iv) truncated moments of a single function of the n th order statistic