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Local limit theorems for the maxima of discrete random variables

Published online by Cambridge University Press:  24 October 2008

C. W. Anderson
Affiliation:
University of Sheffield

Extract

Let , where the Xi, i = 1, 2, … are independent identically distributed random variables. Classical extreme value theory, described for example in the books of do Haan(6) and Galambos(3) gives conditions under which there exist constants an > 0 and bn such that

where G(x) is taken to be one of the extreme value distributions G1(x) = exp (− e−x), G2(x) = exp (− x−a) (x > 0, α > 0) and G3(x) = exp (−(− x)α) (x < 0, α > 0).

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1980

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References

REFERENCES

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