Work

Classification of scaling and translation invariant exponential families on the real line

Year: 2026

Type: article

Abstract: The family of normal distributions on $$\mathbb {R}$$ R is closed under scaling and translation. Another example of an exponential family on $$\mathbb {R}$$ R with this property is the family of exponential-polynomial distributions. We prove that, conversely, an exponential family with such property is essentially the family of exponential-polynomial distributions.

Source: Information Geometry

DOI: 10.1007/s41884-026-00197-4

Authors: Koichi Tojo, Taro Yoshino

Institutions: Tokai University, The University of Tokyo

Language: English

Topic: Probability and Statistical Research

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Japan Society for the Promotion of Science