On the modeling of small sample distributions with generalized Gaussian density in a maximum likelihood framework

The modeling of sample distributions with generalized Gaussian density (GGD) has received a lot of interest. Most papers justify the existence of GGD parameters through the asymptotic behavior of some mathematical expressions (i.e., the sample is supposed to be large). In this paper, we show that the computation of GGD parameters on small samples is not the same as on larger ones. In a maximum likelihood framework, we exhibit a necessary and sufficient condition for the existence of the parameters. We derive an algorithm to compute them and then compare it to some existing methods on random images of different sizes.