Approximating the Rao's distance between negative binomial distributions. Application to counts of marine organisms

International audienceWhile the negative binomial distribution is widely used to model catches of animals, it is noteworthy that the parametric approach is ill-suited from an exploratory point of view. Indeed, the " visual " distance between parameters of several distributions is misleading, since on the one hand it depends on the chosen parametrization and on the other hand these parameters are not commensurable (i. e. they measure quite different characteristics). Consequently, we settle the topic of comparing abundance distributions in a well-suited framework: the Rie-mannian manifold N B(D R) of negative binomial distributions, equipped with the Fisher-Rao metrics. It is then possible to compute an intrinsic distance between species. We focus on computational issues encountered in computing this distance between marine species