On Representations of Divergence Measures and Related Quantities in Exponential Families

Bedbur, Stefan; Kamps, Udo

doi:10.3390/e23060726

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On Representations of Divergence Measures and Related Quantities in Exponential Families

by

Stefan Bedbur

and

Udo Kamps

^*

Institute of Statistics, RWTH Aachen University, 52056 Aachen, Germany

^*

Author to whom correspondence should be addressed.

Entropy 2021, 23(6), 726; https://doi.org/10.3390/e23060726

Submission received: 12 May 2021 / Revised: 3 June 2021 / Accepted: 5 June 2021 / Published: 8 June 2021

(This article belongs to the Special Issue Measures of Information)

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Abstract

Within exponential families, which may consist of multi-parameter and multivariate distributions, a variety of divergence measures, such as the Kullback–Leibler divergence, the Cressie–Read divergence, the Rényi divergence, and the Hellinger metric, can be explicitly expressed in terms of the respective cumulant function and mean value function. Moreover, the same applies to related entropy and affinity measures. We compile representations scattered in the literature and present a unified approach to the derivation in exponential families. As a statistical application, we highlight their use in the construction of confidence regions in a multi-sample setup.

Keywords: exponential family; cumulant function; mean value function; divergence measure; distance measure; affinity

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MDPI and ACS Style

Bedbur, S.; Kamps, U. On Representations of Divergence Measures and Related Quantities in Exponential Families. Entropy 2021, 23, 726. https://doi.org/10.3390/e23060726

AMA Style

Bedbur S, Kamps U. On Representations of Divergence Measures and Related Quantities in Exponential Families. Entropy. 2021; 23(6):726. https://doi.org/10.3390/e23060726

Chicago/Turabian Style

Bedbur, Stefan, and Udo Kamps. 2021. "On Representations of Divergence Measures and Related Quantities in Exponential Families" Entropy 23, no. 6: 726. https://doi.org/10.3390/e23060726

APA Style

Bedbur, S., & Kamps, U. (2021). On Representations of Divergence Measures and Related Quantities in Exponential Families. Entropy, 23(6), 726. https://doi.org/10.3390/e23060726

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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On Representations of Divergence Measures and Related Quantities in Exponential Families

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