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On probability properties of measures of random sets and the asymptotic behavior of empirical distribution functions

Published online by Cambridge University Press:  14 July 2016

Gedalia Ailam
Gedalia Ailam*
Affiliation:
Michigan State University
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Extract

Probability properties of the measure of the union of random sets have theoretical as well as practical importance (David (1950), Garwood (1947), Hemmer (1959)). In the present paper we derive asymptotic properties of the distributions of these measures and apply the derived properties to the investigation of the asymptotic behavior of empirical distribution functions. Thus, an asymptotic distribution function for the relative lengths of steps in the empirical distribution function is obtained.

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 5 , Issue 1 , April 1968 , pp. 196 - 202
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

[1] Ailam, G. (1966) Moment of coverage and coverage spaces. J. Appl. Prob. 3, 550–555.CrossRefGoogle Scholar
[2] David, F. N. (1950) Two combinatorial tests of whether a sample has come from a given population. Biometrica 37, 97–110.Google ScholarPubMed
[3] Garwood, F. (1947) The variance of overlap of geometrical figures with reference to a bombing problem. Biometrika 34, 1–17.CrossRefGoogle ScholarPubMed
[4] Hammer, P. Chr. (1959) A problem of geometrical probabilities. K. norske Vidensk. Selsk. Forh. 32, 117–120.Google Scholar
[5] Loève, M. (1955) Probability Theory. Van Nostrand, New York.Google Scholar
[6] Saks, S. (1937) Theory of the Integral. 2nd Edition. Hafner Publication Co., New York.Google Scholar
[7] Weiss, L. (1955) The stochastic convergence of a function of sample successive differences. Ann. Math. Statist. 26, 532–536.CrossRefGoogle Scholar