General Fisher information matrices of a random vector

We extend the (q,λ)-Fisher information to a much broader setting, where the power function x↦|x|q in the (q,λ)-Fisher information is replaced by an arbitrarily chosen convex function. We describe qualitative research, which is undertaken within the general framework, on the newly-introduced generalized Fisher information. In particular, we derive the characterization of general Fisher information matrix for a random vector in Rn.