Riemann manifolds from Hellinger distance

Hellinger distance provides a way to evaluate how far is a given probability distribution from another one. This kind of tool is well-suited e.g. for target recognition in a radar system. The aim of this paper is to show that, given a couple of probability distributions with a single estimator, the evaluation of their Hellinger distance provides a metric for a Riemann manifold that, being conformal, implies that an estimator can always be found that makes the distance minimal. So, in this case, the choice of the best distribution reduces simply to the computation of this estimator. Finally, applications in the area of target recognition can be devised.