Fitting a distribution to the histograms obtained for a group

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For a group of subjects (n=10), I have a normalized histogram for each subject. Now I am defining a distribution from all these histogram. What would be a reasonable approach to it? E.g., is there a method that I can use to combine all histogram to fit the distribution? Or to fit the distribution to the average of the normalized frequencies across the group?

I will be using R to carry out the analysis.