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A note on the Lévy distance

Published online by Cambridge University Press:  14 July 2016

J. W. Thompson
J. W. Thompson*
Affiliation:
University of Hull
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Abstract

The Lévy distance, L(F,G), between two distribution functions F and G has the important property that convergence of L(Fn,F) is equivalent to convergence in distribution. The fact that L(F,G) is not invariant under a change of scale has been thought to be a disadvantage. However, simple bounds on the Lévy distance between the transformed distribution functions can be found.

Keywords

LĚVY DISTANCESCALE TRANSFORMATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 2 , June 1975 , pp. 412 - 414
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Gnedenko, B. V., and Kolmogorov, A. N. (1954) Limit Distributions for Sums of Independent Random Variables. Addison-Wesley, Reading, Mass.Google Scholar