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Some results on the decomposability of the distribution of quadratic expressions

Published online by Cambridge University Press:  24 October 2008

D. N. Shanbhag
D. N. Shanbhag
Affiliation:
University of Sheffield
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Extract

Recently Davidson (1), Kendall (3) and Shanbhag (7) have established that if U and V are independently distributed random variables such that U is non-degenerate and P(V = 0) < 1, then the distribution of (U2, 2UV, V2) is indecomposable. This implies that the distributions of (U2, 2UV, V2) G and (U2, U) H, where G and H are non-singular real square matrices, are indecomposable. As observed by Shanbhag (7), from this it follows that the Wishart distribution Wp(1, Σ, M) with both p and rank (Σ) ≥ 2 is indecomposable. This is an extension of a result of Lévy (5) who had shown that the distribution Wp(1, Σ, 0) with Σ diagonal is indecomposable.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 77 , Issue 3 , May 1975 , pp. 553 - 558
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

REFERENCES

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