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The variances of a sequence

Published online by Cambridge University Press:  24 October 2008

I. J. Maddox
I. J. Maddox
Affiliation:
Queen's University of Belfast
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Extract

In statistical problems, use is often made of the variance s2 of a finite sequence of numbers x1, x2, …, xn, where

x¯ being the arithmetic mean of x1, x2, …, xn. The object of this note is to introduce a generalized variance for an infinite sequence x = (xk) and to examine some of its properties.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 84 , Issue 1 , July 1978 , pp. 109 - 112
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

REFERENCES

(1)Hardy, G. H.Divergent series (Oxford University Press, 1949).Google Scholar
(2)Lorentz, G. G.A contribution to the theory of divergent sequences. Acta Math. 80 (1948), 167–190.CrossRefGoogle Scholar
(3)Petersen, G. M.Regular matrix transformations (New York, McGraw-Hill, 1966).Google Scholar