In this paper we analyze several strategies for the estimation of the roughness parameter of the $\mathcal G_I^0$ distribution. It has been shown that this distribution is able to characterize a large number of targets in monopolarized SAR imagery, deserving the denomination of "Universal Model" It is indexed by three parameters: the number of looks (which can be estimated in the whole image), a scale parameter, and the roughness or texture parameter. The latter is closely related to the number of elementary backscatters in each pixel, one of the reasons for receiving attention in the literature. Although there are efforts in providing improved and robust estimates for such quantity, its dependable estimation still poses numerical problems in practice. We discuss estimators based on the minimization of stochastic distances between empirical and theoretical densities, and argue in favor of using an estimator based on the Triangular distance and asymmetric kernels built with Inverse Gaussian densities. We also provide new results regarding the heavytailedness of this distribution.