In what form your CPFEM machine presents the distribution in question?  If it produces histograms then your task should be to arrange your observed data into the same form, i.e. to distribute observed values between identical histogram bins.  Your current procedure seems essentially correct, but there is a question how many angular bins should be used.  The practical answer may be found in Kevin H. Knuth, "Optimal Data-Based Binning for Histograms", https://arxiv.org/pdf/physics/0605197  (cited 75 times)

and in later publication by David W. Hogg ([email protected]):

https://www.google.pl/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5&cad=rja&uact=8&ved=0ahUKEwjHt5CU97bOAhUG8RQKHZ8ABegQFghcMAQ&url=http%3A%2F%2Fcosmo.nyu.edu%2Fhogg%2Fresearch%2F2010%2F07%2F27%2Fbinning.pdf&usg=AFQjCNHuXukXc7NjK-fzTELrR6grQrcZsg

I'm sorry I didn't explain the abbreviation - CPFEM stands for Crystal Plasticity Finite Element Method. I have orientation of every element (mean orientation of orientations in integration points), so I can calculate misorientations between two neighbouring elements. But I don't know, how to plot the misorientation distribution of such discrete set.

Try this in Matlab

[count,binval]=hist(Misorientation,40);

ncount=count/sum(count);

bins_interp = linspace(binval(1), binval(end),500);

counts_interp = interp1(binval, ncount, bins_interp, 'spline');

figure(1);

plot(bins_interp, counts_interp,'color',rand(1,3))

* Misorientation (above) should contain the array of discrete values !

By this you would be obtaining a probability distribution function for the discrete values you have by the spline fit.

Thanks,

Prithivi