The exponential family generated by the skew-normal distribution.

The aim of this paper is to consider the SN class of distributions as a member of a broader class of distributions, introducing another structural parameter. The starting point is the study of the Normal curves of the r-th order, (Box, 1953), (Turner, 1960), (Vianelli, 1963), considered also in Azzalini (1986). The arrival point showed in this paper is the obtaining of the exponential family generated by the skew-normal distribution, through the method of exponential tilting introduced by Efron (1981). We proved that this family is an example of extended SN distribution as introduced by Azzalini (1985).