Values from Empirical Distribution Functions

I have an empirical distribution of data, in this case intensity probability versus radius. I can get the values of the maximum radius (end point of the distribution) and most probable radius (radius at maximum intensity probability). I want to obtain values for the mean and rms radii (not the mean and rms of the intensity probability). Before I roll my own functions, am I missing an existing operation or function to get these values?

The analogy is to obtain various moments for the molar mass of a polymer from a distribution function of number of chains versus molar mass of the chain. It is equivalent to the question about radius of gyration in a distribution, which is the second moment of the distribution.

I can't think of an immediate built-in operation or function to compute these.  In general, given pdf(x) you could compute any moment by integrating (in this case you seem to have finite limits [0,R]).  You can compute the n'th moment using Integrate1D where your user function will return, e.g., (x^n)*pdf(x).