Invariant statistics and characterizations of probability distributions

A. L. Rukhin

Leningrad

Abstract: The problem of a characterization of a family of probability measures with group parameter by the distribution of the maximal invariant is considered. For compact groups and plane movements groups, simple sufficient conditions for such a characterization are given.

Received: 12.12.1973

 English version: Theory of Probability and its Applications, 1976, 20:3, 584–598

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