Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-05-11T16:38:39.825Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Research supported by the National Science Foundation under Grant MCS8202259.

References

[1] Balkema, A. A. and De Haan, L. (1978) Limit distributions for order statistics I. Theory Prob. Appl. 23, 77–92.Google Scholar
[2] Balkema, A. A. and De Haan, L. (1978) Limit distributions for order statistics II. Theory Prob. Appl. 23, 341–358.Google Scholar
[3] Bender, E. A. (1974) Asymptotic methods in enumeration. SIAM Rev. 16, 485–515.CrossRefGoogle Scholar
[4] Comtet, L. (1974) Advanced Combinatorics. Riedel, Boston.Google Scholar
[5] David, F. N. and Barton, E. E. (1962) Combinatorial Chance. Griffin, London.Google Scholar
[6] Garsia, A. M. and Gessel, I. (1979) Permutation statistics and partitions. Adv. Math. 31, 288–305.Google Scholar
[7] Rota, G. C. and Mullin, R. (1970) On the foundations of combinatorial theory. In Graph Theory and its Applications, ed. Harris, B., Academic Press, New York.Google Scholar