A Rank Histogram (or Talagrand Diagram) is a neat way of measuring whether your numerical model is giving appropriate variance. It's used for weather and climate forcasting, where you only have one observational series, and many model series (an ensemble). It's described pretty clearly here. Basically, you take a handful of runs of your model, then for each timestep/gridpoint, whatever, you calculate how the observations rank relative to the model ensemble. Then you plot a histogram of those ranks. If the histogram is u-shaped, then variance is too low (obs are rank high or low too often), if the histogram looks kind of gaussian, then the variance is too high (obs rarely ranks high or low), and if the histogram is flat, then your variance is spot-on (obs have a similar variance as the ensemble).
So the question is, which distribution should I fit to this kind of data, and why? The latter part of the question is more important, because I think that the correct distribution is the Beta-binomial distribution, but I'm unfamiliar with this area.