H. Alzer and J. Wells, Inequalities for the polygamma functions, SIAM Journal on Mathematical Analysis, vol.29, issue.6, pp.1459-1466, 1998.

. Shun-ichi-amari, Natural gradient works efficiently in learning, Neural computation, vol.10, issue.2, pp.251-276, 1998.

. Shun-ichi-amari, Information geometry and its applications, vol.194, 2016.

J. Angulo and S. Velasco-forero, Morphological processing of univariate gaussian distributionvalued images based on poincaré upper-half plane representation, Geometric Theory of Information, pp.331-366, 2014.

M. Arnaudon, F. Barbaresco, and L. Yang, Riemannian medians and means with applications to radar signal processing, IEEE Journal of Selected Topics in Signal Processing, vol.7, issue.4, pp.595-604, 2013.

K. Arwini, T. J. Christopher, and . Dodson, Information geometry: near randomness and near independence, 2008.

C. Atkinson and A. Mitchell, Rao's distance measure, Sankhy?: The Indian Journal of Statistics, Series A, pp.345-365, 1981.

N. Ay and J. Jost, Information geometry and sufficient statistics. Probability Theory and Related Fields, vol.162, pp.327-364, 2015.

M. Bauer, M. Bruveris, and P. W. Michor, Uniqueness of the Fisher-Rao metric on the space of smooth densities, Bulletin of the London Mathematical Society, vol.48, issue.3, pp.499-506, 2016.

N. Bouguila, D. Ziou, and J. Vaillancourt, Unsupervised learning of a finite mixture model based on the dirichlet distribution and its application, IEEE Transactions on Image Processing, vol.13, issue.11, pp.1533-1543, 2004.

H. Andrew, . Briggs, M. Ades, and . Price, Probabilistic sensitivity analysis for decision trees with multiple branches: use of the dirichlet distribution in a bayesian framework, Medical Decision Making, vol.23, issue.4, pp.341-350, 2003.

O. Calin and C. Udri?te, Geometric modeling in probability and statistics, 2014.

N. Nikolaevich and C. , Statistical decision rules and optimal inference. transl. math. Monographs, 1982.

A. Ronald and . Fisher, On the mathematical foundations of theoretical statistics, Philosophical Transactions of the Royal Society of London. Series A, vol.222, pp.309-368, 1922.

H. Gene and . Golub, Some modified matrix eigenvalue problems, Siam Review, vol.15, issue.2, pp.318-334, 1973.

T. Griffiths, Gibbs sampling in the generative model of latent dirichlet allocation, 2002.

G. Stephen and . Harris, Closed and complete spacelike hypersurfaces in minkowski space, Classical and Quantum Gravity, vol.5, issue.1, p.111, 1988.

H. Karcher, Riemannian center of mass and mollifier smoothing, Communications on pure and applied mathematics, vol.30, issue.5, pp.509-541, 1977.

. Stefan-l-lauritzen, Statistical manifolds. Differential geometry in statistical inference, vol.10, pp.163-216, 1987.

D. Rasmus-e-madsen, C. Kauchak, and . Elkan, Modeling word burstiness using the dirichlet distribution, Proceedings of the 22nd international conference on Machine learning, pp.545-552, 2005.

Y. Ollivier, True asymptotic natural gradient optimization, 2017.

O. Barrett and . Neill, Semi-Riemannian geometry with applications to relativity, 1983.

D. Philip, . Neill, O. Gareth, and . Roberts, Bayesian inference for partially observed stochastic epidemics, Journal of the Royal Statistical Society: Series A (Statistics in Society, vol.162, issue.1, pp.121-129, 1999.

A. Peter and A. Rangarajan, Shape analysis using the fisher-rao riemannian metric: Unifying shape representation and deformation, 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, pp.1164-1167, 2006.

M. Petrovich, Sur une fonctionnelle, Publ. Math. Beograd, TL, 1932.

. C-radhakrishna-rao, Information and the accuracy attainable in the estimation of statistical parameters, Bull. Calcutta Math. Soc, vol.37, p.1945

S. Rebbah, F. Nicol, and S. Puechmorel, The geometry of the generalized gamma manifold and an application to medical imaging, Mathematics, vol.7, issue.8, p.674, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02159244

S. Said, L. Bombrun, and Y. Berthoumieu, Warped riemannian metrics for location-scale models, Geometric Structures of Information, pp.251-296, 2019.

O. Schwander and F. Nielsen, Model centroids for the simplification of kernel density estimators, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp.737-740, 2012.

S. Lene-theil, A Riemannian geometry of the multivariate normal model, Scandinavian Journal of Statistics, pp.211-223, 1984.

A. Srivastava, I. Jermyn, and S. Joshi, Riemannian analysis of probability density functions with applications in vision, 2007 IEEE Conference on Computer Vision and Pattern Recognition, pp.1-8, 2007.

J. Sy-trimble, . Wells, and . Wright, Superadditive functions and a statistical application, SIAM journal on mathematical analysis, vol.20, issue.5, pp.1255-1259, 1989.

S. Yang and Z. Fang, Beta approximation of ratio distribution and its application to next generation sequencing read counts, Journal of applied statistics, vol.44, issue.1, pp.57-70, 2017.

Z. Yang, Some properties of the divided difference of psi and polygamma functions, Journal of Mathematical Analysis and Applications, vol.455, issue.1, pp.761-777, 2017.

Z. Zhang, H. Sun, and F. Zhong, Information geometry of the power inverse gaussian distribution, Applied Sciences, vol.9, 2007.