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Exact and limiting distribution of sustained maxima

Published online by Cambridge University Press:  14 July 2016

E. R. Canfield  and
W. P. McCormick
E. R. Canfield
Affiliation:
University of Georgia
W. P. McCormick*
Affiliation:
University of Georgia
*
∗ Postal address: Department of Statistics and Computer Science, University of Georgia, Athens, GA 30602, U.S.A.
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Abstract

Define a random variable

We refer to Yn as a sustained maximum. Under the assumption that the Xi 's are i.i.d. the exact distribution of Yn is obtained. Under certain conditions on the underlying distribution F we obtain weak limit results for the Yn as well. Also a combinatorial extreme-value problem is solved.

Keywords

ORDER STATISTICSMAXIMALIMIT DISTRIBUTIONPERMUTATIONSGENERATING FUNCTION

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 4 , December 1983 , pp. 803 - 813
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

Research supported by the National Science Foundation under Grant MCS8202259.

References

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