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11. Musielak, J.: Orlicz spaces and modular spaces. Lecture Notes in Mathematics, vol. 1034.
Springer, Berlin (1983)
12. Naudts, J.: Deformed exponentials and logarithms in generalized thermostatistics. Physica A:
Stat. Mech. Appl. 316(1), 323–334 (2002). https://doi.org/10.1016/S0378-4371(02)01018-X
13. Naudts, J.: Estimators, escort probabilities, and φ-exponential families in statistical physics.
JIPAM. J. Inequal. Pure Appl. Math. 5(4), Article 102, 15 (electronic) (2004)
14. Naudts, J.: Generalised Thermostatistics. Springer, London Ltd, London (2011). https://doi.
org/10.1007/978-0-85729-355-8
15. Naudts, J., Zhang, J.: Rho-tau embedding and gauge freedom in information geometry. Inf.
Geometry 1(1), 79–115 (2018). https://doi.org/10.1007/s41884-018-0004-6
16. Pistone, G.: κ-exponential models from the geometrical viewpoint. Eur. Phys. J. B 70(1), 29–37
(2009). https://doi.org/10.1140/epjb/e2009-00154-y
17. Pistone, G., Rogantin, M.P., et al.: The exponential statistical manifold: mean parameters,
orthogonality and space transformations. Bernoulli 5(4), 721–760 (1999)
18. Pistone, G., Sempi, C.: An infinite-dimensional geometric structure on the space of all the
probability measures equivalent to a given one. Ann. Statist. 23(5), 1543–1561 (1995). https://
doi.org/10.1214/aos/1176324311
19. Santacroce, M., Siri, P., Trivellato, B.: New results on mixture and exponential models by
Orlicz spaces. Bernoulli 22(3), 1431–1447 (2016). https://doi.org/10.3150/15-BEJ698
20. de Souza, D.C., Vigelis, R.F., Cavalcante, C.C.: Geometry induced by a generalization of rényi
divergence. Entropy 18(11), 407 (2016). https://doi.org/10.3390/e18110407
21. Tsallis, C.: Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World,
1st edn. Springer, New York (2009)
22. Umarov, S., Tsallis, C., Steinberg, S.: On a q-central limit theorem consistent with nonextensive
statistical mechanics. Milan J. Math. 76, 307–328 (2008). https://doi.org/10.1007/s00032-0080087-y
23. Vieira, F.L.J., Vigelis, R.F., de Andrade, L.H.F., Cavalcante, C.C.: Deformed exponential and
the behavior of the normalizing function. In: Nielsen, F., Barbaresco, F. (eds.) Geometric
Science of Information, pp. 271–278. Springer International Publishing, Cham (2019)
24. Vigelis, R.F., de Andrade, L.H.F., Cavalcante, C.C.: On the Existence of Paths Connecting
Probability Distributions, pp. 801–808. Springer International Publishing, Cham (2017)
25. Vigelis, R.F., de Andrade, L.H.F., C.Cavalcante, C.: Conditions for the existence of a generalization of Rényi divergence. Physica A: Stat. Mech. Appl. 558, 124953 (2020). https://doi.
org/10.1016/j.physa.2020.124953
26. Vigelis, R.F., Cavalcante, C.C.: The 2 -condition and φ-families of probability distributions.
In: Geometric Science of Information, Lecture Notes in Computer Science, vol. 8085, pp.
729–736. Springer, Heidelberg (2013)
27. Vigelis, R.F., Cavalcante, C.C.: On φ-families of probability distributions. J. Theoret. Probab.
26(3), 870–884 (2013). https://doi.org/10.1007/s10959-011-0400-5
28. Vigelis, R.F., Cavalcante, C.C.: Smoothness of the Orlicz norm in Musielak-Orlicz function
spaces. Math. Nachr. 287(8–9), 1025–1041 (2014)
29. Zhang, J., Hästö, P.: Statistical manifold as an affine space: a functional equation approach. J.
Math. Psych. 50(1), 60–65 (2006). https://doi.org/10.1016/j.jmp.2005.08.003
L. H. F. de Andrade et al.
11. Musielak, J.: Orlicz spaces and modular spaces. Lecture Notes in Mathematics, vol. 1034.
Springer, Berlin (1983)
12. Naudts, J.: Deformed exponentials and logarithms in generalized thermostatistics. Physica A:
Stat. Mech. Appl. 316(1), 323–334 (2002). https://doi.org/10.1016/S0378-4371(02)01018-X
13. Naudts, J.: Estimators, escort probabilities, and φ-exponential families in statistical physics.
JIPAM. J. Inequal. Pure Appl. Math. 5(4), Article 102, 15 (electronic) (2004)
14. Naudts, J.: Generalised Thermostatistics. Springer, London Ltd, London (2011). https://doi.
org/10.1007/978-0-85729-355-8
15. Naudts, J., Zhang, J.: Rho-tau embedding and gauge freedom in information geometry. Inf.
Geometry 1(1), 79–115 (2018). https://doi.org/10.1007/s41884-018-0004-6
16. Pistone, G.: κ-exponential models from the geometrical viewpoint. Eur. Phys. J. B 70(1), 29–37
(2009). https://doi.org/10.1140/epjb/e2009-00154-y
17. Pistone, G., Rogantin, M.P., et al.: The exponential statistical manifold: mean parameters,
orthogonality and space transformations. Bernoulli 5(4), 721–760 (1999)
18. Pistone, G., Sempi, C.: An infinite-dimensional geometric structure on the space of all the
probability measures equivalent to a given one. Ann. Statist. 23(5), 1543–1561 (1995). https://
doi.org/10.1214/aos/1176324311
19. Santacroce, M., Siri, P., Trivellato, B.: New results on mixture and exponential models by
Orlicz spaces. Bernoulli 22(3), 1431–1447 (2016). https://doi.org/10.3150/15-BEJ698
20. de Souza, D.C., Vigelis, R.F., Cavalcante, C.C.: Geometry induced by a generalization of rényi
divergence. Entropy 18(11), 407 (2016). https://doi.org/10.3390/e18110407
21. Tsallis, C.: Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World,
1st edn. Springer, New York (2009)
22. Umarov, S., Tsallis, C., Steinberg, S.: On a q-central limit theorem consistent with nonextensive
statistical mechanics. Milan J. Math. 76, 307–328 (2008). https://doi.org/10.1007/s00032-0080087-y
23. Vieira, F.L.J., Vigelis, R.F., de Andrade, L.H.F., Cavalcante, C.C.: Deformed exponential and
the behavior of the normalizing function. In: Nielsen, F., Barbaresco, F. (eds.) Geometric
Science of Information, pp. 271–278. Springer International Publishing, Cham (2019)
24. Vigelis, R.F., de Andrade, L.H.F., Cavalcante, C.C.: On the Existence of Paths Connecting
Probability Distributions, pp. 801–808. Springer International Publishing, Cham (2017)
25. Vigelis, R.F., de Andrade, L.H.F., C.Cavalcante, C.: Conditions for the existence of a generalization of Rényi divergence. Physica A: Stat. Mech. Appl. 558, 124953 (2020). https://doi.
org/10.1016/j.physa.2020.124953
26. Vigelis, R.F., Cavalcante, C.C.: The 2 -condition and φ-families of probability distributions.
In: Geometric Science of Information, Lecture Notes in Computer Science, vol. 8085, pp.
729–736. Springer, Heidelberg (2013)
27. Vigelis, R.F., Cavalcante, C.C.: On φ-families of probability distributions. J. Theoret. Probab.
26(3), 870–884 (2013). https://doi.org/10.1007/s10959-011-0400-5
28. Vigelis, R.F., Cavalcante, C.C.: Smoothness of the Orlicz norm in Musielak-Orlicz function
spaces. Math. Nachr. 287(8–9), 1025–1041 (2014)
29. Zhang, J., Hästö, P.: Statistical manifold as an affine space: a functional equation approach. J.
Math. Psych. 50(1), 60–65 (2006). https://doi.org/10.1016/j.jmp.2005.08.003