Comparison of the performances of our maximum likelihood estimator for the estimation of the column densities (Cols. #2 and #3) and the couple (T_kin, $n_{{\text{H}}_2}$) (Cols. #4 and #5) and for two examples of kinetic temperature and volume density. The first example (Cols. #2 and #4) at medium density and warm temperature. The second one (Cols. #3 and #5) at high density and colder temperature. In the first and second rows we estimate the parameters with the ¹³CO lines, and the (¹³CO, C¹⁸O) lines, respectively. In the last three rows we estimate the parameters with the lines of the three main CO isotopologues. In the last two rows we biased one of the parameters for the ¹²CO RADEX model to test the effect of incorrect physical assumptions in the estimator. The kinetic temperature and volume density of the ¹²CO RADEX model is biased in the fourth row, while the ratio of abundances of ¹²CO and ¹³CO is biased to a smaller values than assumed in the estimator on the fifth row. In all panels, the modeled and biased values of the estimated parameters are shown with the red and black crosses, respectively. The red ellipses, computed with the Cramér-Rao bound, are confidence ellipses (CE) of efficient estimations with a probability of 99%. The green points shows the estimated values for 200 simulated spectra. The color images on Cols. #3 and #4 show the values of the negative log-likelihood for the couple (T_kin, $n_{{\text{H}}_2}$) that our estimator assumes to be common to all analyzed species. The vertical dotted line are the effective critical density of the different transitions.