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A new formula for cumulants

Published online by Cambridge University Press:  24 October 2008

I. J. Good
I. J. Good
Affiliation:
Virginia Polytechnic Institute and State University
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Extract

Let θ be an n-dimensional random vector with components θ1, θ2, …, θn and let itscumulants

be defined as usual by the identity

where x1, x2, …, xn are purely imaginary variables, E denotes expectation, and

Let θ(1), θ(2), …, θ(R) be independent and identically distributed (i.i.d.) random vectors each with the same distribution as θ, where R = r1 + r2 + … + rn = |r|, the order of the cumulant Kr. Let θ* have the components

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 78 , Issue 2 , September 1975 , pp. 333 - 337
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

REFERENCES

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