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.
Original language | Undefined |
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Pages (from-to) | 133-162 |
Number of pages | 30 |
Journal | Mathematical methods of statistics |
Volume | 14 |
Issue number | 2 |
Publication status | Published - 2005 |
Keywords
- EWI-12818
- MSC-62E20
- MSC-62G30
- Control charts
- convolutions Tail behavior
- IR-62325
- MSC-62P30