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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

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