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Embedding sequences of successive maxima in extremal processes, with applications

Published online by Cambridge University Press:  14 July 2016

Rocco Ballerini  and
Sidney I. Resnick
Rocco Ballerini*
Affiliation:
University of Florida
Sidney I. Resnick
Affiliation:
Colorado State University
*
∗Postal address: Department of Statistics, University of Florida, Gainesville, FL 32611, USA.
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Abstract

Consequences of embedding sequences {Mn} in an extremal-F process are discussed where Mn represents the maximum of n independent (but not necessarily identically distributed) random variables. Various limit theorems are proved for the sample record rate, record times, inter-record times, and record values. These results are illustrated with applications to three particular record models: the Yang (1975) record model where population size increases geometrically, a record model where linear improvement is present, and a record model incorporating features of the previous two.

Keywords

RECORDSGUMBEL DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 4 , December 1987 , pp. 827 - 837
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

This work was partially supported by a Research Development Award at the University of Florida.

∗∗

Present address: Cornell University, OR/IE, Upson Hall, Ithaca, NY14853, USA.

Initially supported by NSF Grant DMS 8202335 and at the end by a UK Science and Engineering Research Council Fellowship at Sussex University.

References

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