Thank you very much for reply.

I suspected that chi-squared and p-Value are to be calculated separately from procedure of fitting with NonlinearModelFit function, and none of its available options can cover this.

My situation seems to be quite common in the tasks of data analysis.

I have an experimental dataset (with their errors), and theoretical function to fit them. I need to find the fitting parameters of theoretical function and a quality of this fit (what is the probability that this fit is true).

I use:

NonlinearModelFit[Data, {Function[a,b,x], a_min<a<a_max, b_min<b<1-a_max}, {{a,a_seed},{b,b_seed}}, x, Weights->1/Errors^2]

Function is given by some integral. (In general, there are more fitting parameters, but they break fitting.)

It seemed to me, that "EstimatedVariance coincides with chi^2 value, but it does not look so.

The p-values, which are available in ParameterTable", relate, as i understand, to probability of fitting parameters confidence interval, but not to a quality of the fit itself.

But i need a probability that the fit itself is true.

I would be grateful for any clarifications of these points.