The Rao's distance between negative binomial distributions for Exploratory Analyses and Goodness-of-Fit Testing

International audienceThe statistical analysis of counts of living organisms brings information about the collective behavior of species (schooling, habitat preference, etc), possibly depending on their biological characteristics (growth rate, reproductive power, survival rate, etc). The negative binomial distribution (NB) is widely used to model such data but the parametric approach is ill-suited from an exploratory point of view. Indeed, the visual distance between parameters is not relevant, because it depends on the chosen parametrization! On the contrary, considering the Riemannian manifold N B(D R) of negative binomial distributions equipped with the Fisher-Rao metrics, it is possible to compute intrinsic distances between species. In this work, we focus on geometrical aspects of the χ 2 goodness-of-t (GOF) test for distributions in N B(D R), in connection with the position of the reference distribution. We show that this position is critical for performances of this test, as Critchley & Marriott (2016) noticed in a dierent setting