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February, 1965 One-Parameter Exponential Families Generated by Transformation Groups
R. Borges, J. Pfanzagl
Ann. Math. Statist. 36(1): 261-271 (February, 1965). DOI: 10.1214/aoms/1177700287


We consider a one-parameter exponential family generated by an arbitrary group of transformations of an abstract sample space. Topological assumptions about the group are not required. It is shown that such a family has densities either of the type of the normal distribution or of the type of the gamma distribution with respect to an invariant measure. This is a generalization of results of Dynkin (1951), Lindley (1958) and Ferguson (1962 and 1963).


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R. Borges. J. Pfanzagl. "One-Parameter Exponential Families Generated by Transformation Groups." Ann. Math. Statist. 36 (1) 261 - 271, February, 1965.


Published: February, 1965
First available in Project Euclid: 27 April 2007

zbMATH: 0134.14802
MathSciNet: MR176563
Digital Object Identifier: 10.1214/aoms/1177700287

Rights: Copyright © 1965 Institute of Mathematical Statistics

Vol.36 • No. 1 • February, 1965
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