Tail behavior of the empirical distribution function of convolutions

Willem/Wim Albers, W.C.M. Kallenberg

    Research output: Contribution to journalArticleAcademicpeer-review


    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.
    Original languageUndefined
    Pages (from-to)133-162
    Number of pages30
    JournalMathematical methods of statistics
    Issue number2
    Publication statusPublished - 2005


    • EWI-12818
    • MSC-62E20
    • MSC-62G30
    • Control charts
    • convolutions Tail behavior
    • IR-62325
    • MSC-62P30

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