  We discuss the Bohmian mechanics by means of the deformed Schr\"odinger
equation for position dependent mass, in the context of a $q$-algebra inspired
by nonextensive statistics. A deduction of the Bohmian quantum formalism is
performed by means of a deformed Fisher information functional, from which a
deformed Cram\'er-Rao bound is derived. Lagrangian and Hamiltonian
formulations, inherited by the $q$-algebra, are also developed. Then, we
illustrate the results with a particle confined in an infinite square potential
well. The preservation of the deformed Cram\'er-Rao bound for the stationary
states shows the role played by the $q$-algebraic structure.
