  We present an alternative method to analyse cosmic microwave background (CMB)
maps. We base our analysis on the study of the partition function. This
function is used to examine the CMB maps making use of the different
information embedded at different scales and moments. Using the partition
function in a likelihood analysis in two dimensions (Q_rms,n), we find the
best-fitting model to the best data available at present the COBE--DMR 4 years
data set. By means of this analysis we find a maximum in the likelihood
function for n=1.8 (-0.65 +0.35) and Q_rms-PS = 10 (-2.5 +3) muK (95 %
confidence level) in agreement with the results of other similar analyses
(Smoot et al. 1994 (1 yr), Bennet et al. 1996 (4 yr)). Also making use of the
partition function we perform a multifractal analysis and study the possible
fractal nature of the CMB sky. We find that the measure used in the analysis is
not a fractal. Finally, we use the partition function for testing the
statistical distribution of the COBE--DMR data set. We conclude that no
evidence of non-Gaussianity can be found by means of this method.
