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arXiv · 1401.4419

On Edgeworth Expansions in Generalized Urn Models

Sh. M. Mirakhmedov·S. Rao Jammalamadaka·Ibrahim B. Mohamed
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Abstract

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.

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Sh. M. Mirakhmedov, S. Rao Jammalamadaka, Ibrahim B. Mohamed. 2014-01-17. On Edgeworth Expansions in Generalized Urn Models. https://doi.org/10.1007/s10959-012-0454-z

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