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Poisson process and distribution-free statistics

Published online by Cambridge University Press:  01 July 2016

Meyer Dwass
Meyer Dwass*
Affiliation:
Northwestern University, Evanston, Illinois
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Abstract

The well-known connection between the Poisson process and empirical c.d.f.'s is exploited from a new point of view. Distributions of functions of empirical c.d.f.'s for finite sample size n are explicitly described in some new examples, and new qualitative information is obtained for some classical examples.

Keywords

POISSON PROCESSEMPIRICAL CDFKOLMOGOROV-SMIRNOV STATISTICSDISTRIBUTION-FREE STATISTICS
Type
Research Article
Information
Advances in Applied Probability , Volume 6 , Issue 2 , June 1974 , pp. 359 - 375
Copyright
Copyright © Applied Probability Trust 1974 

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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.Google Scholar
[2] Birnbaum, Z. W. and Pyke, R. (1958) On some distributions related to the statistic Dn + . Ann. Math. Statist. 29, 179–187.Google Scholar
[3] Dempster, A. P. (1959) Generalized Dn + statistics. Ann. Math. Statist. 30, 593–597.CrossRefGoogle Scholar
[4] Dwass, M. (1959) The distribution of a generalized Dn + statistic. Ann. Math. Statist. 30, 1024–1028.CrossRefGoogle Scholar
[5] Kolmogorov, A. N. (1933) Sulla determinazione empirica de una legge de distribuzione. Giorn. Inst. Ital. Attuari 4, 83–91.Google Scholar
[6] Massey, F. J. Jr. (1950) A note on the estimation of a distribution function by confidence limits. Ann. Math. Statist. 21, 116–119.Google Scholar
[7] Pyke, R. (1959) The supremum and infimum of the Poisson process. Ann. Math. Statist. 30, 568–576.Google Scholar
[8] Smirnov, N. V. (1939) On the derivations of the empirical distribution curve. Mat. Sbornik 6 (48), 1, 3–26. In Russian.Google Scholar