In this paper, two different mathematical methods are used to derive skew distributions.
The results generalize Azzalini (1985) and FernĀ“andez and Steel (1998) skew distributions
generating new results in general, and skew normal distribution in particular. Some mathematical
properties, such as n-th moments, distribution function, moments generating function,
are also given for the generalizations. Some known and new special cases are also
mentioned. Some graphs for skew distributions are included. Results are applied to two
practical problems. Shannon and Renyi entropies as well as Fisher information are also
obtained.