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Records from improving populations

Published online by Cambridge University Press:  14 July 2016

Rocco Ballerini and
Sidney Resnick
Rocco Ballerini*
Affiliation:
Colorado State University
Sidney Resnick*
Affiliation:
Colorado State University
*
Postal address for both authors: Department of Statistics, Colorado State University, Fort Collins, CO 80523, USA.
Postal address for both authors: Department of Statistics, Colorado State University, Fort Collins, CO 80523, USA.
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Abstract

We consider records from the sequence Yj = Xj, + cj, j ≧ 1 where c > 0 if upper records are of interest and c < 0 if lower records are studied. If {Xj } is stationary the record rate is asymptotically constant and if {Xj } is i.i.d. the record rate is, in addition, asymptotically normal. These results are illustrated by analysis of the times in the mile run.

Keywords

TRENDSSUBADDITIVE ERGODIC THEORYSTATIONARY SEQUENCESARMA MODELSCENTRAL LIMIT THEOREM

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 3 , September 1985, pp. 487 - 502
Copyright
Copyright © Applied Probability Trust 1985 

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Footnotes

∗

Partially supported by NSF Grants CEE 8110782 and DMS 8202335.

∗∗

Partially supported by NSF Grant DMS 8202335.

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