Tail behavior of the empirical distribution function of convolutions

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Albers, W. and Kallenberg, W.C.M. (2004) Tail behavior of the empirical distribution function of convolutions. [Report]

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Abstract:
Control charts based on convolutions require study of the tail behavior of the empirical distribution function of convolutions. It is well-known that this empirical distribution function at a fixed argument $x$ is asymptotically normal. The asymptotic normality is extended here to sequences $x_{n}$ tending to infinity at a suitable rate. At still larger $x_{n}$'s Poisson limiting distributions come in for the classical empirical distribution function. Surprisingly, this property does not generalize to its convolution counterpart, since for those $x_{n}$'s it is degenerate at $0$ with probability tending to 1. Exact inequalities for the tail behavior are presented as well.
Item Type:Report
Additional information:Imported from MEMORANDA
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/65924
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