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Functions of a statistical variate with given means, with special reference to Laplacian distributions

Published online by Cambridge University Press:  24 October 2008

M. C. K. Tweedie
M. C. K. Tweedie
Affiliation:
Radiotherapeutic CentreAddenbrooke's HospitalCambridge
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Extract

A method is described in general terms for finding the function of a variate of which the mean is a given function of a parameter of the population. This can sometimes be used for finding unbiased estimates and for finding the moments and moment-generating functions of a statistic when another statistic based on the same observations has a constant value. It is always available when the latter statistic is a ‘sufficient statistic’ for estimating the parameter, which requires the frequency function to be of a certain form. A number of examples are given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 43 , Issue 1 , January 1947 , pp. 41 - 49
Copyright
Copyright © Cambridge Philosophical Society 1947

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References

REFERENCES

(1)Kendall, M. G.The advanced theory of statistics, 1 (Griffin, London, 1945), §§ 1·16–1.22.Google Scholar
(2)Bartlett, M. S.J. London Math. Soc. 13 (1938), 62.CrossRefGoogle Scholar
(3)Fisher, R. A.Proc. London Math. Soc. (2) 30 (1928), 199.Google Scholar
(4)Tweedie, M. C. K.J. London Math. Soc. (in the Press).Google Scholar
(5)Cochran, W. G.Ann. Eugen., Lond., 7 (1936), 207.CrossRefGoogle Scholar
(6)Fisher, R. A.Proc. Roy. Soc. A, 144 (1934), 285.Google Scholar
(7)Koopman, B. O.Trans. American Math. Soc. 39 (1936), 399.CrossRefGoogle Scholar
(8)Tweedie, M. C. K.Nature, Lond., 156 (1945), 453.CrossRefGoogle Scholar
(9)Aitken, A. C. and Silverstone, H.Proc. Roy. Soc. Edinburgh, A, 61 (1942), 186.Google Scholar
(10)Wilks, S. S.Mathematical statistics (Princeton University Press, 1943), § 5–23.Google Scholar
(11)Whittaker, E. T. and Robinson, G.Calculus of observations (Blackie, London, 1924), § 88.Google Scholar
(12)McKay, A. T.Biometrika, 24 (1932), 38.Google Scholar
(13)Haldane, J. B. S.Nature, Lond., 155 (1945), 49.Google Scholar