A two-parameter family of non-parametric, deformed exponential manifolds

Abstract We construct a new family of non-parametric statistical manifolds by means two-parameter class deformed exponential functions, that includes functions with power-law, linear and sublinear rates growth. The are modelled on weighted, mixed-norm Sobolev spaces especially suited to this purpose, in the sense an important nonlinear superposition operators (those used construction divergences tensors) act continuously them. analyse variants these operators, map into “subordinate” spaces, evaluate associated gain regularity. With appropriate choice parameter values, support large variety entropies appearing literature, as well their tensors, eg. Fisher-Rao metric. Manifolds finite measures probability constructed; latter shown be smoothly embedded submanifolds former.