Spline approximations of the Lambert W function and application to simulate generalized Gaussian noise with exponent α=1/2α=1/2

In this paper we focus on the problem of synthesizing a generalized Gaussian noise with exponent 1/2 using the inverse transform of the cumulative distribution function (c.d.f.). It has been previously shown that this inverse can be written in terms of the Lambert W function. We have developed a new procedure to evaluate this special function using spline functions. Based on this method, we present techniques to generate generalized Gaussian noise with exponent 1/2. It is observed that the method developed in this paper is better than the approach of Chapeau-Blondeau and Monir.