Advances in the characterization of curvature of two-dimentional probability manifolds

In this work some advances in the theory of curvature of two-dimensionalprobability manifolds corresponding to families of distributions are proposed.It is proved that location-scale distributions are hyperbolic in theInformation Geometry sense even when the generatrix is non-even or non-smooth.A novel formula is obtained for the computation of curvature in the case ofexponential families: this formula implies some new flatness criteria indimension 2. Finally, it is observed that many two parameter distributions,widely used in applications, are locally hyperbolic, which highlights the roleof hyperbolic geometry in the study of commonly employed probability manifolds.These results have benefited from the use of explainable computational tools,which can substantially boost scientific productivity.