One-Parameter Exponential Families Generated by Transformation Groups

Borges, R.; Pfanzagl, J.

Borges, R. ; Pfanzagl, J.

Ann. Math. Statist., Tome 36 (1965) no. 6, p. 261-271 / Harvested from Project Euclid

Résumé

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).

Publié le : 1965-02-14
Classification:

@article{1177700287,
     author = {Borges, R. and Pfanzagl, J.},
     title = {One-Parameter Exponential Families Generated by Transformation Groups},
     journal = {Ann. Math. Statist.},
     volume = {36},
     number = {6},
     year = {1965},
     pages = { 261-271},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177700287}
}

Borges, R.; Pfanzagl, J. One-Parameter Exponential Families Generated by Transformation Groups. Ann. Math. Statist., Tome 36 (1965) no. 6, pp.  261-271. http://gdmltest.u-ga.fr/item/1177700287/