Abstract
The aim of this work is to prove that the Amari manifold of beta distributions of the first kind distribution have dual potential, dual coordinate pairs and his corresponding gradient system is linearizable and Hamiltonian.
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References
Amari, S.: Differential-Geometrical Methods in Statistics. 2nd Printing, vol. 28. Springer Science, Tokyo (2012). https://doi.org/10.1007/978-1-4612-5056-2
Barbaresco, F.: Jean-Louis Koszul and the elementary structures of information geometry. In: Nielsen, F. (ed.) Geometric Structures of Information. Signals and Communication Technology, pp. 333–392. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-02520-5-12
Barbaresco, F.: Les densités de probabilité distinguées et l’équation d’Alexis Clairaut: regards croisés de Maurice Fréchet et de Jean-Louis Koszul. GRETSI (2017). http://gretsi.fr/colloque2017/myGretsi/programme.php
Barbaresco, F.: Science géométrique de l’Information: Géométrie des matrices de covariance, espace métrique de Fréchet et domaines bornés homogénes de Siegel. C mh 2(1), 1–188 (2011)
Barbaresco, F.: La géometrie de l’information des systemes dynamiques de Jean -Louis Koszul et Jean-Marie Souriau: thermodynamique des groupes de lie et métrique de Fisher-Koszul-Souriau. Thales (1), 1–7 (1940–1942)
Fujiwara, A.: Dynamical systems on statistical models (state of art and perspectives of studies on nonliear integrable systems). RIMS Kôkyuroku 822, 32–42 (1993). http://hdl.handle.net/2433/83219
Nakamura, Y.: Completely integrable gradient systems on the manifolds of Gaussian and multinomial distributions. Jpn. J. Ind. Appl. Math. 10(2), 179–189 (1993). https://doi.org/10.1007/BF03167571
Calin, O., Udrişte, C.: Geometric Modeling in Probability and Statistics, vol. 121. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-07779-6
Acknowledgements
I gratefully acknowledge all my discussions with members of ERAG of the University of Maroua. Thanks are due to Dr. Kemajou Theophile for fruitful discussions.
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Mama Assandje, P.R., Dongho, J. (2023). Geometric Properties of Beta Distributions. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science, vol 14071. Springer, Cham. https://doi.org/10.1007/978-3-031-38271-0_21
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DOI: https://doi.org/10.1007/978-3-031-38271-0_21
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