A new class of distribution function based on the symmetric densities is introduced, these transformations also produce nonnormal distributions and its pdf and cd f can be expressed in parametric form.This class of distributions depend on the two parameters, namely g and h which controls the skewness and the elongation of the tails, respectively.This class of skewed distributions is a generalization of Tukey's gh family of distributions.In this paper, we calculate a closed form expression for the density and distribution of the Tukey's gh family of generalized distributions, which allows us to easily compute probabilities, moments and related measures.