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On the rate of convergence in a local limit theorem†

Published online by Cambridge University Press:  24 October 2008

Sujit K. Basu
Sujit K. Basu
Affiliation:
Indian Statistical Institute, Calcutta, India
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Extract

Let Zn = n−½(X1 + X2 + … + Xn), where {Xn} is a sequence of independent and identically distributed random variables with EX1 = 0, and a common distribution function F and characteristic function ω. Suppose |ω|r is integrable for some integer r ≥ 1. For all n ≥ r, then Zn has a probability density function fn obtained by using the inversion formula.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 1 , July 1974 , pp. 307 - 312
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

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