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Quadratic forms in Poisson and multi-nomial variables

Published online by Cambridge University Press:  09 April 2009

P. Whittle
P. Whittle
Affiliation:
Applied Mathematics Laboratory, New Zealand, D.S.I.R., (present address: Statistical Laboratory, Cambridge University).
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Summary

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Let represent the deviations from expectation of a set of multinomial or independent Poisson variables, and Η be a positive definite matrix. A lower bound is obtained for Pr in terms of Pr, Where is a vector of normal variables with the same mean and covariance matrix as Δ.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 1 , Issue 2 , February 1960 , pp. 233 - 240
Copyright
Copyright © Australian Mathematical Society 1960

References

[1]Cochran, W. G. (1952). The χ2 test of goodness of fit. Ann. Math. Stat., 23, 315–45.CrossRefGoogle Scholar
[2]Darwin, J. H. (1958). On corrections to the χ2 distribution. J. Roy. Stat. Soc., B. 20, 387–392.Google Scholar
[3]Hoel, P. G. (1938). On the Chi-square distribution for small samples. Ann. Math. Stat., 9, 158–65.CrossRefGoogle Scholar
[4]Wilton, J. R. (1929). The lattice points of the circle: an historical account of the problem. Messenger of Math., 58, 67–80.Google Scholar