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On the joint distribution of the number of upper and lower records and the number of inversions in a random sequence

Published online by Cambridge University Press:  01 July 2016

W. Katzenbeisser
W. Katzenbeisser*
Affiliation:
Institute of Statistics, Vienna
*
∗Postal address: Institut für Statistik der Wirtschaftsuniversität Wien, A-1090 Wien, Augasse 2-6, Austria.
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Abstract

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Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 22 , Issue 4 , December 1990 , pp. 957 - 960
Copyright
Copyright © Applied Probability Trust 1990 

References

Anderson, E. Sparre (1954) On the fluctuation of sums of random variables. Math. Scand. 2, 171–181.Google Scholar
Brunk, H. D. (1960) On a theorem of E. Sparre Andersen and its application to tests against trend. Math. Scand. 4, 305–326.CrossRefGoogle Scholar
Comtet, L. (1972) Advanced Combinatorics. D. Reidel, Dordrecht.Google Scholar
David, F. N. and Barton, D. E. (1962) Combinatorial Chance. Griffin, London.CrossRefGoogle Scholar
Foster, F. G. and Stuart, A. (1954) Distribution-free tests in time-series based on the breaking of records. J. R. Statist. Soc. 16, 1–22.Google Scholar
Haghighi-Talab, D. and Wright, C. (1973) On the distribution of records in a finite sequence of observations, with an application to road traffic problems. J. Appl. Prob. 10, 556–571.CrossRefGoogle Scholar
Katzenbeisser, W. (1988) On the joint distribution of the random variables number of inversions and number of outstanding variables in a randomly arranged sequence. Statistical Papers 29, 133–144.CrossRefGoogle Scholar
Kemp, R. (1984) Fundamentals of the Average Case Analysis of Particular Algorithms . Wiley, New York; Teubner, Stuttgart.CrossRefGoogle Scholar
Knuth, D. E. (1969) The Art of Computer Programming , Vol. 1. Addison-Wesley, Reading, Mass. Google Scholar
Panny, W. (1986) A note on the higher moments of the expected behavior of straight insertion sort. Inf. Proc. Lett. 22, 175–177.CrossRefGoogle Scholar
Pfeifer, D. (1989) Extremal processes, secretary problems and the 1/e law. J. Appl. Prob. 26, 722–733.CrossRefGoogle Scholar
Renyi, A. (1962) Théorie des éléments saillants d'une suite d'observations. Proc. Coll. Comb. Methods in Prob. Th. Aarhus University, 104–115.Google Scholar
Resnick, S. I. (1973) Record values and maxima. Ann. Prob. 1, 650–662.CrossRefGoogle Scholar
Shorrock, R. (1972) On record values and record times. J. Appl. Prob. 9, 316–326.CrossRefGoogle Scholar
Shorrock, R. (1973) Record values and inter-record times. J. Appl. Prob. 10, 543–555.CrossRefGoogle Scholar
Shorrock, R. (1974) On discrete time extremal processes. Adv. Appl. Prob. 6, 580–592.CrossRefGoogle Scholar