[…] The cumulative distribution function for the generalized Gaussian distribution does not have a closed-form solution in terms of elementary functions. However, there are a few values of α for which the equations simplify, including α=1/2. Chapeau-Blondeau and Monir (2002) note that the generalized Gaussian distribution with α=1/2 is especially useful in practice because its quantile function (inverse CDF) can be explicitly expressed in terms of the Lambert W function. …