On Edgeworth Expansions in Generalized Urn Models

S. M. Mirakhmedov (), S. Rao Jammalamadaka () and Ibrahim B. Mohamed ()
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S. M. Mirakhmedov: Institute of Mathematics and Information Technologies
S. Rao Jammalamadaka: University of California
Ibrahim B. Mohamed: University of Malaya

Journal of Theoretical Probability, 2014, vol. 27, issue 3, 725-753

Abstract: Abstract The random vector of frequencies in a generalized urn model can be viewed as conditionally independent random variables, given their sum. Such a representation is exploited here to derive Edgeworth expansions for a “sum of functions of such frequencies,” which are also called “decomposable statistics.” Applying these results to urn models such as with- and without-replacement sampling schemes as well as the multicolor Pólya–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.

Keywords: Edgeworth expansion; Urn models; Sampling with and without replacement; Pólya–Egenberger model; Poisson distribution; Binomial distribution; Negative binomial distribution; Chi-square statistic; Sample sum; Dixon statistic; 62G20; 60F05 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10959-012-0454-z

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