Performances of the approximate forms of the covariance matrix in terms of rigenvalues and χ²-distributions. Top panel: eigenvalues of the covariance matrices (rebinned into six bins) compared to what can be obtained from the proposed approximate forms; same color-coding as for Fig. 6. The χ² distributions are shown in the bottom panel. Model (86) reproduces the very same χ² distributions. Model (85), in gray, is not as accurate and tends to slightly overestimate the χ². This latter behavior is amplified when a larger number of bins is used.