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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.

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

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