Fitting a distribution?

Question

I'm trying to fit a sample to an established distribution (normal, exp, etc.). I know there are stuff like goodness of fits (chi-square, Kolmogorov and stuff). But I'm wondering if there exists an index of fit that says how much the curve fits to the data (i.e., how much, like percent, the model accounts for the variance of the data). And not just a p-value to accept or reject it...

Answer 1

You should look at R-squared, also known as the coefficient of determination.  The wikipedia article on that is a good source.

Basically R^2 gives the fraction of the variance that is explained by the model -- more or less (this is true only for certain kinds of models -- more precisely it is 1 minus the fraction of the unexplained variance)

To calculate it, set R^2 = 1 - SSe/SSt

Here, SSe is the sum-of-squares of the error = sum[(sample value i - model predicted value i)^2]

and SSt is the total sum-of-squares = sum[(sample value i - the sample mean)^2]