I have circular data -- observations each of which falls between -180 degrees and +180 degrees -- divided into a 15-bin histogram.
I'd like to see how well a continuous PDF -- specifically a mixture of a von Mises distribution and a uniform distribution, with particular parameters -- fits the observed histogram.
And to determine this fit, I'd like to use the r-squared statistic. I'd like to leave aside the question of whether I should be using r-squared or something else. My choice of r-squared is based on Zhang & Luck, Nature, 2008 and Zhang & Luck, Psychological Science, 2009, work I'm trying to replicate. (These papers did exactly what I'm describing I want to do -- compute the r-squared between a 15-bin histogram of circular data and the mixture model.) But if you'd like to suggest a better method, and can describe it clearly, I'd be happy to try it out.
My question is, how should I compute the r-squared? Should I bin the continuous function, and then compare the PDF bin heights to the observed bin heights? Should I take the mean of the PDF over the range spanned by each bin of the observed data? Should I compare the bin centers to the corresponding points in the continuous function?