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The use of a ballot theorem in order statistics

Published online by Cambridge University Press:  14 July 2016

Lajos Takács
Lajos Takács*
Affiliation:
Columbia University, New York
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Extract

The following generalization of the classical ballot theorem has many possible applications in order statistics.

Type
Short Communications
Information
Journal of Applied Probability , Volume 1 , Issue 2 , December 1964 , pp. 389 - 392
Copyright
Copyright © Applied Probability Trust 

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References

[1] Birnbaum, Z. W. and Tingey, F. H. (1951) One sided confidence contours for probability distribution functions. Ann. Math. Statist. 22, 592–596.CrossRefGoogle Scholar
[2] Chang, Li-Chien (1955) On the ratio of an empirical distribution function to the theoretical distribution function. (Chinese) Acta. Math. Sinica 5, 347–368. English translation: Selected Translations in Mathematical Statistics and Probabilitity. American Mathematical Society (1963) 4, 17-38.Google Scholar
[3] Daniels, H. E. (1945) The statistical theory of the strength of bundles of threads. I. Proc. Roy. Soc. A 183, 405–435.Google Scholar
[4] Dempster, A. P. (1945) Generalized Dn+ statistics. Ann. Math. Statist. 30, 593–597.CrossRefGoogle Scholar
[5] Dwass, M. (1959) The distribution of a generalized Dn+ statistic. Ann. Math. Statist. 30, 1024–1028.CrossRefGoogle Scholar
[6] Ishii, G. (1959) On the exact probabilities of Rényi's tests. Ann. Inst. Statist. Math. Tokyo 11, 17–24.CrossRefGoogle Scholar
[7] Robbins, H. (1954) A one-sided confidence interval for an unknown distribution funcion (abstract). Ann. Math. Statist. 25, 409.Google Scholar
[8] Smirnov, N. V. (1944) Approximate laws of distribution of random variables from tempirical data. (Russian) Uspehi Mat. Nauk 10, 179–206.Google Scholar
[9] Smirnov, N. V. (1961) The probability of large values on non-parametric one-sided criteria of fit. (Russian) Trudy Mat. Inst. Steklov 64, 185–210.Google Scholar
[10] TakáCs, L. (1962) The time dependence of a single-server queue with Poisson input and general service times. Ann. Math. Statist. 33, 1340–1348.CrossRefGoogle Scholar
[11] TakáCs, L. (1964) Combinatorial methods in the theory of dams. J. Appl. Prob. 1, 69–76.CrossRefGoogle Scholar