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A Note on Normal Attraction to a Stable Law

Published online by Cambridge University Press:  20 November 2018

M. V. Menon  and
V. Seshadri
M. V. Menon
Affiliation:
University of Missouri, Columbia Missouri
V. Seshadri
Affiliation:
McGill University, Montreal, Quebec
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Let X1, X2, …, be a sequence of independent and identically distributed random variables, with the common distribution function F(x). The sequence is said to be normally attracted to a stable law V with characteristic exponent α, if for some an (converges in distribution to V). Necessary and sufficient conditions for normal attraction are known (cf [1, p. 181]).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 3 , September 1971 , pp. 451 - 452
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Gnedenko, B.V. and Kolmogorov, A. N., Limit distributions for sums of independent random variables, Addison-Wesley, Reading, Mass., 1954.Google Scholar