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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.
M. C. K. Tweedie (Wed,) studied this question.
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