What about Monte Carlo? I recently produced (with help from contributors to this list) qq plots for certain complicated mixtures of distributions. To evaluate goodness of fit, I produced Monte Carlo confidence intervals from 401 simulated qq plots and took the 11th and 391st of them for each quantile. {quantile(1:401, c(.025, .975)) = c(11, 391)}. Something like this could be done to obtain a significance level for ks.test, for example.

This may not be as satisfying for some purposes as a clean, theoretical result, but it produced useful answers without busting the project budget too badly.

hope this helps. spencer graves

roger koenker wrote:

In full generality this is a quite difficult problem as discussed in
Durbin's (1973) SIAM monograph.  An elegant general approach
is provided by Khmaladze

@article{Khma:Arie:1981,
author = {Khmaladze, E. V.},
title = {Martingale approach in the theory of goodness-of-fit tests},
year = {1981},
journal = {Theory of Probability and its Applications (Transl of Teorija Verojatnostei i ee Primenenija)},
volume = {26},
pages = {240--257}
}


but I don't think that there is a general implementation of the approach for R, or
any other software environment, for that matter.


url:    www.econ.uiuc.edu/~roger            Roger Koenker
email    [EMAIL PROTECTED]            Department of Economics
vox:     217-333-4558                University of Illinois
fax:       217-244-6678                Champaign, IL 61820

On Jun 29, 2004, at 1:08 PM, Christian Hennig wrote:

Hi,

is there any method for goodness of fit testing of an (as general as
possible) univariate distribution with parameters estimated, for normal,
exponential, gamma distributions, say (e.g. the corrected p-values for
the Kolmogorov-Smirnov or Chi-squared with corresponding ML estimation
method)?
It seems that neither ks.test nor chisq.test handle estimated parameters.
I am aware of function goodfit in package vcd, which seems to it for some
discrete distributions.


Thank you for help,
Christian


*********************************************************************** Christian Hennig Fachbereich Mathematik-SPST/ZMS, Universitaet Hamburg [EMAIL PROTECTED], http://www.math.uni-hamburg.de/home/hennig/ ####################################################################### ich empfehle www.boag-online.de

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