An extension of the generalized Gaussian distribution to include asymmetry

The generalized Gaussian distribution, under the control of two parameters, can describe a family of an infinite number of probability distributions—e.g. the Laplace, the Gaussian, etc.—all of which are symmetric distributions. To allow for asymmetric distributions, an extension of the generalized Gaussian distribution is proposed here. The proposed extension, under the control of three parameters, can describe the generalized Gaussian distribution as well as an infinite number of asymmetric distributions of varying asymmetry and tail lengths.