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Fisher information, Borges operators, and q-calculus |
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| Authors: | F. Pennini A. Plastino |
| Affiliation: | a Departamento de Física, Universidad Católica del Norte, Casilla 1280, Antofagasta, Chile b Exact Sciences Faculty, National University La Plata, Argentina’s National Research Council (IFLP-CCT-CONICET), C.C. 727, (1900) La Plata, Argentina c Facultad de Ciencias Exactas, Universidad Nacional de La Pampa, Peru y Uruguay, Santa Rosa, La Pampa, Argentina |
| Abstract: | 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]. |
| Keywords: | 05.30.-d 03.65.-w 05.40.-a |
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