I have a large sets of real-world user data (30k, 80k, 90k measurements). To be precise those are simply session lengths for a specific system. I want to create a theoretical model of this, to generate session lengths that roughly follow the distribution of the real-world session lengths (to be used in simulations).
I fitted the data to a Weibull distribution, which visually worked very well. When I create sample data from the Weibull distribution, using the parameters from the fitting, I get data that is very, very close.
However, when I want to test the goodness of the fit, things don't look so good. At first I used the K-S test (first value is D, second value is p-value)
K-S test = (0.044257085422165915, 6.1787818394288534e-160) 2-sample K-S test = (0.044934832227649907, 9.8401466055748469e-83)
The D-values are pretty low, which is nice. But the p-values are abysmal. Further research lead me to this answer, which - if I understand correctly - states, that a K-S test might not be the best tool for my case. The thing is, that the real-world data simply does not follow a specific, theoretical distribution. So the p-values should be low. What I want is just a distribution that generates values that are pretty close to the real world data.
Is there any renowned test that supports me in finding a distribution that is pretty close?