  The random vector of frequencies in a generalized urn model is viewed as
conditionally independent random variables, given their sum. Such a
representation is exploited to derive Edgeworth expansions for a sum of
functions of such frequencies. Applying these results to urn models such as
with- and without-replacement sampling schemes as well as the multicolor
Polya-Egenberger model, new results are obtained for the chi-square statistic,
for the sample sum in a without replacement scheme, and for the so-called Dixon
statistic that is useful in comparing two samples.
