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Some remarks on nevzorov's record model

Published online by Cambridge University Press:  01 July 2016

Dietmar Pfeifer
Dietmar Pfeifer*
Affiliation:
University of Oldenburg
*
∗Postal address: Fachbereich 6, Mathematik, Universität Oldenburg, Postfach 25 03, D-W2900 Oldenburg, Germany.
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Abstract

We give a simple proof for the independence of record indices in Nevzorov's record model which is based on ranks. An application of these results to a probabilistic analysis of a particular searching algorithm with non-equiprobable orderings is also discussed.

Keywords

RECORD INDEXRANKSPOISSONBINOMIALDISTRIBUTIONNON-EQUIPROBABLEORDERINGSSEARCHING ALGORITHM
Type
Research Article
Information
Advances in Applied Probability , Volume 23 , Issue 4 , December 1991 , pp. 823 - 834
Copyright
Copyright © Applied Probability Trust 1991 

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References

Dansie, B. R. (1983) A note on permutation probabilities. J. R. Statist. Soc. 45, 22–24.Google Scholar
Deheuvels, P. and Pfeifer, D. (1988) On a relationship between Uspensky's theorem and Poisson approximation. Ann. Inst. Statist. Math. 40, 671–681.CrossRefGoogle Scholar
Hartigan, J. A. (1968) Note on discordant observations. J. R. Statist. Soc. 30, 545–550.Google Scholar
Harville, D. A. (1973) Assigning probabilities to the outcomes of multi-entry competitions. J. Amer. Statist. Assoc. 68, 312–316.CrossRefGoogle Scholar
Kemp, R. (1984) Fundamentals of the Average Case Analysis of Particular Algorithms. Wiley–Teubner, New York and Stuttgart.CrossRefGoogle Scholar
Knuth, D. W. (1973) The Art of Computer Programming. Vol. 1: Fundamental Algorithms . Addision-Wesley, Reading, MA.Google Scholar
Nevzorov, V. B. (1986) Two characterizations using records. In Stability Problems for Stochastic Models. Lecture Notes in Mathematics 1233, Springer-Verlag, 79–85.Google Scholar
Nevzorov, V. B. (1988) Records. Theory Prob. Appl. 32, 201–228.CrossRefGoogle Scholar
Pfeifer, D. (1987) On a joint strong approximation theorem for record and inter-record times. Prob. Theory Rel. Fields 75, 213–221.CrossRefGoogle Scholar
Pfeifer, D. (1989a) Einführung in die Extremwertstatistik. Teubner-Verlag, Stuttgart.CrossRefGoogle Scholar
Pfeifer, D. (1989b) Extremal processes, secretary problems and the 1/e law. J. Appl. Prob. 26, 722–733.CrossRefGoogle Scholar
Plackett, R. L. (1968) Random permutations. J. R. Statist. Soc. 30, 517–534.Google Scholar
Plackett, R. L. (1975) The analysis of permutations. Appl. Statist. 24, 193–202.CrossRefGoogle Scholar
Rényi, A. (1962) Théorie des éléments saillants d'une suite d'observations. Colloquium on Combinatorial Methods in Probability Theory , 104–115, Mathematisk Institut, Aarhus Universitet, Denmark.Google Scholar
Resnick, S. I. (1987) Extreme Values, Regular Variations and Point Processes. Springer, New York.CrossRefGoogle Scholar