Finding the FWHM of a super-Gaussian like data set - any ideas?

Hi all, I've got some sets of data that look like this:

I'm saying super-Gaussian because that's what I think best describes it (see http://slac.stanford.edu/cgi-wrap/getdoc/slac-pub-6684.pdf), but feel free to correct me! I'd like to write a script in MATLAB to find each one's Full Width at Half Maximum. I've found a few ideas online already, but they rely on there being one data point at the peak. I think I'd be looking for something that can average the top points above an upper threshold and the baseline ones below a lower threshold, then work from there. Any tips? I've not used MATLAB for a while so I'm a little rusty. Thanks in advance!