Based on a two-parameter generalization of Gauss’ law of error, a generalized log-likelihood is related to a Bregman divergence. This relation is a two-parameter generalization of the well-known relation between log-likelihood and Kullback–Leibler divergence.
REFERENCES
1.
R. A.
Fisher
, Statistical Methods for Research Workers
(Oliver and Boyd
, Edinburgh
, 1925
).2.
3.
4.
J.
Naudts
, Rev. Math. Phys.
16
, 809
(2004
);5.
F.
Topsøe
, AIP Conf. Proc.
965
, 104
(2007
).6.
L. M.
Bregman
, USSR Comput. Math. Math. Phys.
7
, 200
(1967
).7.
D.
Petz
, Acta Math. Hungar.
116
, 127
(2007
).8.
C. F.
Gauß
, Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium
(F. Perthes and I. H. Besser
, Hamburg
, 1809
).9.
E. T.
Jaynes
, Probability Theory: The Logic of Science
, edited by G. L.
Bretthorst
(Cambridge University Press
, Cambridge
, 2003
).10.
11.
H.
Suyari
and M.
Tsukada
, IEEE Trans. Inf. Theory
51
, 753
(2005
).12.
T.
Wada
and H.
Suyari
, Phys. Lett. A
348
, 89
(2006
).13.
G.
Kaniadakis
, M.
Lissia
, and A. M.
Scarfone
, Physica A
340
, 41
(2004
).14.
B. D.
Sharma
and L. J.
Taneja
, Metrika
22
, 205
(1975
);D. P.
Mittal
, Metrika
22
, 35
(1975
).15.
A. M.
Scarfone
, H.
Suyari
, and T.
Wada
, Cent. Eur. J. Phys.
7
, 414
(2009
).16.
C.
Tsallis
, J. Stat. Phys.
52
, 479
(1988
).17.
G.
Kaniadakis
, Physica A
296
, 405
(2001
).18.
T.
Wada
and H.
Suyari
, Phys. Lett. A
368
, 199
(2007
).© 2009 American Institute of Physics.
2009
American Institute of Physics
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