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Fiducial distribution of several parameters with application to a normal system

Published online by Cambridge University Press:  24 October 2008

Irving E. Segal
Irving E. Segal
Affiliation:
Princeton University, U.S.A.
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Extract

The notion of fiducial probability was introduced by R. A. Fisher and is now widely used in statistical work involving a single unknown parameter. Fisher has also considered the joint fiducial distribution of several parameters for which there exists a sufficient set of statistics, and has derived the fiducial distribution of the two parameters of the one-variate normal law*. Since Fisher's account is brief, we give a more extended description of the fiducial distribution of several independent parameters possessing a sufficient set of statistics.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 34 , Issue 1 , January 1938 , pp. 41 - 47
Copyright
Copyright © Cambridge Philosophical Society 1938

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References

* Fisher, R. A., “The fiducial argument in statistical inference”, Annals of Eugenics, 6 (1935), 391.CrossRefGoogle Scholar

* It is not difficult to show that any function of the u's and a's which has a distribution independent of the a's must be a function of the u's alone.

* Fisher, R. A., “Two new properties of mathematical likelihood”, Proc. Roy. Soc. 144 (1934), 285.CrossRefGoogle Scholar

† Bartlett, M. S., “The information available in small samples”, Proc. Cambridge Phil. Soc. 32 (1936), 560.CrossRefGoogle Scholar

‡ See Eisenhart, , Continuous groups (Princeton, 1933), p. 9.Google Scholar

* Wishart, J. and Bartlett, M. S., “The generalized product moment distribution in a normal system”, Proc. Cambridge Phil. Soc. 29 (1933), 260.CrossRefGoogle Scholar