C. Manté, S. O. Kidé, ;. Colubi, A. Blanco, C. Gatu et al., Approximating the Rao's distance between negative binomial distributions. Application to counts of marine organisms, in: Proceedings of COMPSTAT, p.3747, 2016.

M. Berger, A Panoramic View of Riemannian Geometry, 2003.

C. Manté, J. P. Durbec, and J. C. Dauvin, A functional data-analytic approach to the classication of species according to their spatial dispersion. Application to a marine macrobenthic community from the Bay of Morlaix, Journal of Applied Statistics, vol.32, p.831840, 2005.

S. O. Kidé, C. Manté, L. Dubroca, H. Demarcq, and B. Mérigot, SpatioTemporal Dynamics of Exploited Groundsh Species Assemblages Faced to Environmental and Fishing Forcings: Insights from the Mauritanian Exclusive Economic Zone, PLOS ONE, vol.10, p.141566, 2015.

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, p.18, 2007.

V. Seguy and M. Cuturi, Principal Geodesic Analysis for Probability Measures under the Optimal Transport Metric

, Advances in Neural Information Processing Systems, vol.28, p.33123320, 2015.

C. I. Bliss and R. A. Fisher, Fitting the Negative Binomial distribution to biological data, Biometrics, vol.9, p.176200, 1953.

M. F. O'neill and M. J. Faddy, Use of binary and truncated negative binomial modelling in the analysis of recreational catch data, Fisheries Research, vol.60, p.471477, 2003.

L. Vaudor, N. Lamouroux, and J. Olivier, Comparing distribution models for small samples of overdispersed counts of freshwater sh, Acta Oecologica-International Journal of Ecology, vol.37, p.170178, 2011.

C. Manté, S. O. Kidé, A. Yao-lafourcade, and B. Merigot, Fitting the truncated negative binomial distribution to count data. A comparison of estimators, with an application to groundshes from the Mauritanian Exclusive Economic Zone, Environmental and Ecological Statistics, vol.23, p.000382017300002, 2016.

R. A. Fisher, A. Corbet, and C. B. Williams, The relation between the number of species and the number of individuals in a random sample of an animal population, J. anim. Ecol, vol.12, p.4258, 1943.

F. J. Anscombe, Sampling theory of the negative binomial and logarithmic series distributions, Biometrika, vol.36, p.358382, 1950.

D. G. Kendall, On some modes of population growth leading to R. A. Fisher's logarithmic series distribution, Biometrika, vol.35, p.615, 1948.

C. B. Williams, The Logarithmic Series and its application to biological problems, Journal of Ecology, vol.34, p.253272, 1947.

C. R. Rao, Information and the Accuracy Attainable in the Estimation of Statistical Parameters, Resonance-Journal of Science Education, vol.20, p.7890, 2015.

C. R. Rao, Comment to Kass' paper, vol.4, p.229231, 1989.

K. M. Carter, R. Raich, W. G. Finn, and A. O. Hero, Ieee Transactions on Pattern Analysis and Machine Intelligence, vol.31, pp.2093-195, 2009.

G. Galanis, P. C. Chu, G. Kallos, Y. Kuo, and C. T. Dodson, Wave height characteristics in the north Atlantic ocean: a new approach based on statistical and geometrical techniques, vol.26, p.83103, 2012.

C. T. Dodson, Some illustrations of information geometry in biology and physics, Handbook of research on computational science and engineering, p.287315, 2012.

M. Cubedo, A. Minarro, and J. M. Oller, A dissimilarity based on relevant population features, Journal of Statistical Planning and Inference, vol.143, p.346355, 2013.

I. Ilea, L. Bombrun, C. Germain, I. Champion, R. Terebes et al., Statistical Hypothesis Test for Maritime Pine Forest Sar Images Classication Based on the Geodesic Distance, 2015 IEEE International Geoscience and Remote Sensing Symposium (igarss), pp.3215-3218, 2015.

R. E. Kass, The geometry of asymptotic inference, Statistical Science, vol.4, p.188234, 1989.

M. Menendez, D. Morales, L. Pardo, and M. Salicru, Statistical Tests Based on Geodesic Distances, vol.8, p.6569, 1995.

M. Cubedo and J. M. Oller, Hypothesis testing: a model selection approach, Journal of Statistical Planning and Inference, vol.108, p.321, 2002.

J. Burbea and C. R. Rao, Informative geometry of probality spaces, Expo. Math, vol.4, p.347378, 1986.

S. Amari, H. Nagaoka, and D. Harada, Methods of information geometry, number 191 in Translations of mathematical monographs, nachdr, 2007.

A. Gray, Modern dierential geometry of curves and surfaces with Mathematica, 1998.

M. P. Carmo, Riemannian geometry, Mathematics. Theory & applications, 1992.

J. I. Itoh and T. Sakai, Cut loci and distance functions, Math. J. Yokohama Univ, vol.49, p.6592, 2007.

K. C. Chua and S. H. Ong, Test of misspecication with application to negative binomial distribution, Computational Statistics, vol.28, p.9931009, 2013.

M. Abramowicz and I. A. Stegun, Handbook of mathematical functions with formulas, graphs and mathematical tables, 2002.

W. R. Inc and . Mathematica, , 2017.

M. Majsnerowska, A note on Poisson approximation by w-functions, Applicationes mathematicae, vol.25, p.387392, 1998.

R. Sering, Nonparametric multivariate descriptive measures based on spatial quantiles, Journal of Statistical Planning and Inference, vol.123, p.259278, 2004.

G. Lebanon, Metric learning for text documents, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.28, p.497508, 2006.

J. Benasseni, M. B. Dosse, and S. Joly, On a General Transformation Making a Dissimilarity Matrix Euclidean, Journal of Classication, vol.24, p.304, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00458704

F. Caillez, The analytic solution of the Additive Constant problem, Psychometrika, vol.48, p.305308, 1983.

S. Joly and G. L. Calvé, Etude des puissances d'une distance, Statistique et Analyse des Données, vol.11, p.3050, 1986.

F. Bavaud, On the Schoenberg transformations in data analysis: Theory and illustrations, Journal of Classication, vol.28, p.297314, 2011.

C. Tricot, Courbes et dimension fractale, 2, 1999.