### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 25 |

Publication status | Published - 2004 |

### Publication series

Name | Memorandum Faculty of Applied Mathematics |
---|---|

Publisher | Department of Applied Mathematics, University of Twente |

No. | 1740 |

ISSN (Print) | 0169-2690 |

### Keywords

- MSC-62E20
- EWI-3560
- IR-65924
- MSC-62P30
- METIS-219690
- MSC-62G30

### Cite this

*Tail behavior of the empirical distribution function of convolutions*. (Memorandum Faculty of Applied Mathematics; No. 1740). Enschede: University of Twente, Department of Applied Mathematics.

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*Tail behavior of the empirical distribution function of convolutions*. Memorandum Faculty of Applied Mathematics, no. 1740, University of Twente, Department of Applied Mathematics, Enschede.

**Tail behavior of the empirical distribution function of convolutions.** / Albers, Willem/Wim; Kallenberg, W.C.M.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - Tail behavior of the empirical distribution function of convolutions

AU - Albers, Willem/Wim

AU - Kallenberg, W.C.M.

N1 - Imported from MEMORANDA

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

KW - MSC-62E20

KW - EWI-3560

KW - IR-65924

KW - MSC-62P30

KW - METIS-219690

KW - MSC-62G30

M3 - Report

T3 - Memorandum Faculty of Applied Mathematics

BT - Tail behavior of the empirical distribution function of convolutions

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -