We use the moment method to describe the SED

Sum of SED of modified blackbodies derived from sum of modified black body SED's with three different distribution of parameters T and the slope. For the slope "alpha" we draw from a Gaussian with a mean at 1. For temperature we draw from a two Gaussians centered at 9.75 K and 15.7 K. For "NARROW" and "WIDE" SED models we basically draw from distributions with narrow and larger widths respectively. The "DELTA" SED model corresponds to a modified black body with slope=1 and T=15.7 K. The specific parameter distributions and the resultant SED's are depicted in the figures below:

The figures below indicate how well differnet order moment fits perform on the different SED models:

The figures below show the relative errors

Results from analysis on Colin's SED performed by interpolating on the SED:

Results from analysis on Marcelo's SED performed by interpolating on the SED: