Determine goodness of fit for user defined PDF data.

Hi,

I have some data, and I needed to find the PDF that best fits the data. I was able to figure that out by testing all possible distributions in MATLAB and ranking them based on an AIC or BIC criteria. But now I am required to determine the goodness of fit of the selected PDF using

• The sum of squares due to error (SSE)
• R-square
• Adjusted R-square
• Root mean squared error (RMSE)

Now I have the actual values used to plot the PDF. How can I used this vector of PDF values to check for a goodness of fit against the original data. From my understanding, the fit function only allows you to check goodness of fit using a known polynomial.

[Robert Maurer]

There's an app on MATLAB called "curve fitting tool" this will give you the R-square, SSE, RMSE, and adjusted R-square

[Micah Mungal]

Yeah I am aware but this seems to check for goodness of fit againts some known model. What I have are two vectors, one for the PDF generated using the pdf function in MATLAB and the other from the histogram method.

Answer 1

[Jeff Miller]

The measures you list (SSE, R-square, etc) are not measures of the goodness of fit of a PDF to a data set. You can find a helpful list of possible measures for that in this Wikipedia page, under the heading "Fit of Distributions".

I haven't used the curve fitting toolbox, but my impression is that it is not designed for fitting PDFs, but rather for fitting models to predict one variable from others (e.g., regression).