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Exact and limiting distribution of sustained maxima

  • E. R. Canfield (a1) and W. P. McCormick (a1)

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.

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Corresponding author

Postal address: Department of Statistics and Computer Science, University of Georgia, Athens, GA 30602, U.S.A.

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Research supported by the National Science Foundation under Grant MCS8202259.

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References

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[1] Balkema, A. A. and De Haan, L. (1978) Limit distributions for order statistics I. Theory Prob. Appl. 23, 7792.
[2] Balkema, A. A. and De Haan, L. (1978) Limit distributions for order statistics II. Theory Prob. Appl. 23, 341358.
[3] Bender, E. A. (1974) Asymptotic methods in enumeration. SIAM Rev. 16, 485515.
[4] Comtet, L. (1974) Advanced Combinatorics. Riedel, Boston.
[5] David, F. N. and Barton, E. E. (1962) Combinatorial Chance. Griffin, London.
[6] Garsia, A. M. and Gessel, I. (1979) Permutation statistics and partitions. Adv. Math. 31, 288305.
[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.

Keywords

Exact and limiting distribution of sustained maxima

  • E. R. Canfield (a1) and W. P. McCormick (a1)

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