  In this paper, we provide the R\'enyi entropy and complexity measure for a
novel, flexible class of skew-gaussian distributions and their related
families, as a characteristic form of the skew-gaussian Shannon entropy. We
give closed expressions considering a more general class of closed
skew-gaussian distributions and the weighted moments estimation method. In
addition, closed expressions of R\'enyi entropy are presented for extended
skew-gaussian and truncated skew-gaussian distributions. Finally, additional
inequalities for skew-gaussian and extended skew-gaussian R\'enyi and Shannon
entropies are reported.
