Weighted Relative Group Entropies and Associated Fisher Metrics
Keyword(s):
A large family of new α-weighted group entropy functionals is defined and associated Fisher-like metrics are considered. All these notions are well-suited semi-Riemannian tools for the geometrization of entropy-related statistical models, where they may act as sensitive controlling invariants. The main result of the paper establishes a link between such a metric and a canonical one. A sufficient condition is found, in order that the two metrics be conformal (or homothetic). In particular, we recover a recent result, established for α=1 and for non-weighted relative group entropies. Our conformality condition is “universal”, in the sense that it does not depend on the group exponential.
2013 ◽
Vol 149
(5)
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pp. 754-772
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1972 ◽
Vol 30
◽
pp. 132-133
1997 ◽
Vol 21
(1-2)
◽
pp. S505-S510
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Keyword(s):