let me ask you a very simple question genius and im sure you will google it.
what about goodness of fit what exactly do you think about that with your curve fit model
I think its an interesting question.. when you are fitting probability distributions, its not called a curve fit since its a stochastic model, its called a calibration and estimation. Curve fitting would be when you do something naive like fit a polynomial/Bezeire curve to a price series and try to extrapolate into the future with no economic model or ideas behind it.Trying to make point estimates or something
So yes, model could be miscalibrated or misspecified, but its not, its a pretty good fit, there are other better fitting models that I havent implemented yet. When you study statistics you do maximum likelihood inference, and it lets you compare hypothesis .
So yeah, you need to calibrate your model on the appropriately chosen length of data, or find some way to fuse data into estimates as the data happens (Kalman filtering and the extensions thereof)
Do you even stastics? Have you ever taken a wad of numbers and found out what distribution describes it best out of a set of alternatives?
You know you can take an emperical histogram, and then show the theoretical probabiltiies, and the closer they match the better the model is right?