  I present here a generalization of the maximum likelihood method and the
$\chi^2$ method to the cases in which the data are {\it not} assumed to be
Gaussian distributed. The method, based on the multivariate Edgeworth
expansion, can find several astrophysical applications. I mention only two of
them. First, in the microwave background analysis, where it cannot be excluded
that the initial perturbations are non-Gaussian. Second, in the large scale
structure statistics, as we already know that the galaxy distribution deviates
from Gaussianity on the scales at which non-linearity is important. As a first
interesting result I show here how the confidence regions are modified when
non-Gaussianity is taken into account.
