ONE-PARAMETER EXPONENTIAL FAMILIES GENERATED BY TRANSFORMATION GROUPS,

Abstract

Consider a one-parameter exponential family generated by an arbitrary group of transformations of an abstract sample space. It is shown without topological assumptions about the group that such a family has either densities of the type of the normal distribution or of the type of the gamma distribution with respect to an invariant measure. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1963
Accession Number
AD0424684

Entities

People

  • J. Pfanzagl
  • Rafael Brandão de Rezende Borges

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Distribution Functions
  • Functions (Mathematics)
  • Normal Distribution

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Graph Algorithms and Convex Optimization.

Technology Areas

  • Space