Fisher information, Borges operators, and q-calculus

We discuss applying the increasingly popular q-calculus, or deformed calculus, so as to suitably generalize Fisher’s information measure and the Cramer–Rao inequality. A q-deformation can be attained in multiple ways, and we show that most of them do not constitute legitimate procedures. Within such a context, the only completely acceptable q-deformation is that ensuing from using the so-called Borges derivative [E.P. Borges, Physica A 340 (2004) 95].