MATLAB: Gamfit confidence intervals

distributionstatistics

Hi,
when using the gamfit function, the confidence intervals of the parameters of the gamma distribution are not symmetric around the fitted values. This can be seen for the second (scale) variable in the example given in the R2011b documentation, and seems to apply also to the first (shape) parameter in my R2008b version.
The confidence interval is usually computed using the Fisher Information Matrix, and should be symmetric, as it is given as "fitted value +- c*std" where std is the standard deviation and c a numerical constant giving the desired confidence level under the assumption of normal distribution.
So why isn't the fitted value in the middle of the confidence interval? Are the fitted parameters different from those given and a non-linear transformation is then used for conversion?

Best Answer

GAMFIT fits the parameters on the log scale, on which the asymptotic normal approximation tends to need fewer observations to be reasonable. Then the symmetric CIs for logged parameters get exponentiated. If you edit GAMFIT, you can see exactly what the code does, e.g., lines 279-284 in the current release.
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