  In this work, goodness-of-fit tests are adapted and applied to CMB maps to
detect possible non-Gaussianity. We use Shapiro-Francia test and two Smooth
goodness-of-fit tests: one developed by Rayner and Best and another one
developed by Thomas and Pierce. The Smooth tests test small and smooth
deviations of a prefixed probability function (in our case this is the
univariate Gaussian). Also, the Rayner and Best test informs us of the kind of
non-Gaussianity we have: excess of skewness, of kurtosis, and so on. These
tests are optimal when the data are independent. We simulate and analyse
non-Gaussian signals in order to study the power of these tests. These
non-Gaussian simulations are constructed using the Edgeworth expansion, and
assuming pixel-to-pixel independence. As an application, we test the
Gaussianity of the MAXIMA data. Results indicate that the MAXIMA data are
compatible with Gaussianity. Finally, the values of the skewness and kurtosis
of MAXIMA data are constrained by |S| \le 0.035 and |K| \le 0.036 at the 99%
confidence level.
