A practical procedure to estimate the shape parameter in the generalized Gaussian distribution

We propose a method to estimate the shape parameter p in the generalized Gaussian distribution. Our estimator is an explicit approximate solution to the trascendental estimator obtained by the method of moments. An estimator for p, based on the method of moments, does not always exist, however we show that it is possible to find such an estimator with high probability for most of the practical situations. A numeric-analytical procedure to obtain the confidence intervals for p is also presented. We illustrate our procedures on data obtained from the different subbands of the audio MP3 encoder.