On the parameter space derived from the joint probability density functions and the property of its scalar curvature (Q1901401)

The authors consider a vector of independent, not identically distributed random variables. The density of each component is parametrized by a different parameter. The common distribution together with its Fisher information forms a Riemannian space. In the paper it is called extended parameter space, which allows to study the geodesic distances between the different marginal distributions. The authors interpret it as a new method. The main result is that the scalar curvature of the extended parameter space is the sum of the scalar curvatures of the spaces of the marginal distributions.