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Products of distribution functions attracted to extreme value laws

Published online by Cambridge University Press:  14 July 2016

Sidney I. Resnick
Sidney I. Resnick*
Affiliation:
Technion—Israel Institute of Technology
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Abstract

When is the product of the d.f.'s H 1(·), ···, Hm (·) attracted to an extreme value law φ(x)? We associate with each Hi (·) its A-function Hi (x) is attracted to φ(x) if each Hi (x) is in the domain of attraction of φ(x) and Ai (z) ~ Aj (z), 1 ≦ i, j ≦ m. Equivalence of A-functions determines an equivalence relation which partitions the domain of attraction of φ(x)into one or more convex sets. These sets fail to be closed under passages to the limit (complete convergence).

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 4 , December 1971 , pp. 781 - 793
Copyright
Copyright © Applied Probability Trust 1971 

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