Coefficient of Determinant

R² quantifies the absolute difference between model and measurements it is NOT related to the distribution type.

You may say that the standard deviation and the probability density are related to the distribution type but not R²

It is not limited to a linear regression, to be simple look at EXCEL, when you make a regression not only linear the program gives automatically the different coefficients for the law you choose AND a value for R² which indicates how near is the approximating curve to the measures. It is the correlation coefficient. It is also recommended that an approximation law with an R² less 0.7...0.8 is not good and an other approach has to be done. You notice that the differences are at power 2 for the computation, this is to avoid the wrong interpretation if differences are big but about same on each side of the curve. Squaring eliminates the sign effect. It is also possible to define a uncertainty band using same differences and assuming a probabilistic distribution for them. If you accept for them the normal distribution then you can compute the standard deviation and determine the ± x*σ band within which the measures could (always probability) may be fall.