  In (Hansen et al. 2002) we presented a new approach for measuring
non-Gaussianity of the Cosmic Microwave Background (CMB) anisotropy pattern,
based on the multivariate empirical distribution function of the spherical
harmonics a_lm of a CMB map. The present paper builds upon the same ideas and
proposes several improvements and extensions. More precisely, we exploit the
additional information on the random phases of the a_lm to provide further
tests based on the empirical distribution function. Also we take advantage of
the effect of rotations in improving the power of our procedures. The suggested
tests are implemented on physically motivated models of non-Gaussian fields;
Monte-Carlo simulations suggest that this approach may be very promising in the
analysis of non-Gaussianity generated by non-standard models of inflation. We
address also some experimentally meaningful situations, such as the presence of
instrumental noise and a galactic cut in the map.
