Picking things at random doesn't have to mean they fit a uniform PDF. Is there any reason to think this distribution only makes sense for a finite range of values? Is this distribution actually the sum of a uniform distribution, and some kind of peaked distribution? Neither tail of your data is tending to 0 quickly, perhaps there is an underlying distribution providing 39k counts per channel? Over a finite range, a sum of uniform and beta distribution might look like this. Is a resonance phenomenon at work? A Cauchy distribution (one name for it, which happens to have a Perl module for it) has a mode and median, but is so heavily tailed it has no central moments.