I have some data from manufacturing concerning the variability of certain geometric dimensions of a given machine. These are real numbers (diameters, angles, lengths, etc.), so the variables are continuous. I need to perform an uncertainty quantification study of the performance of the machine: I want to propagate the manufacturing process variability across the chain of codes which are used to compute the performance of the machine, in order to estimate the uncertainty in the machine performance. I thus need to perform a Monte Carlo analysis (or Polynomial Chaos, or Gaussian Process - pick your favourite tool). In a way or the other, I need to be able to sample from a distribution. The distribution is not normal, nor it can reasonably be approximated by a normal distribution: see preceding discussion
I've been advised to try to characterize the data distribution. How do I do that? Is there a standard procedure, or can you suggest useful references? I'm not an expert (as you probably can tell), so I need something simple. I can code in R, I am familiar with the Monte Carlo standard error and I can run hypothesis tests (for example, I understand when to reject normality based on the result of an Anderson-Darling test). I don't know about more advanced stuff, but I'm a good learner, though :)
PS I imagine that characterizing the data distribution means to fit different distributions to my data and find the best fitting one. However, I've heard that this is a kind of data-dredging (I guess because fitting would favor distributions with more parameters), so I imagine there's more to this problem.