Draft #1 On a (β, q)-generalized Fisher information and inequalities involving q-Gaussian distributions

On a (β,q)-generalized Fisher information and inequalities involving q-Gaussian distributions

On a (\beta,q)-generalized Fisher information and inequalities involving q-Gaussian distributions

On a (β, q)-generalized Fisher information and inequalities involving q-Gaussian distributions a) In the present paper, we would like to draw attention to a possible generalized Fisher information that fits well in the formalism of nonextensive thermostatistics. This generalized Fisher information is defined for densities on R n. Just as the maximum Rényi or Tsallis entropy subject to an ellipt...

On generalized Cramér-Rao inequalities, generalized Fisher informations and characterizations of generalized q-Gaussian distributions

This paper deals with Cramér-Rao inequalities in the context of nonextensive statistics and in estimation theory. It gives characterizations of generalized q-Gaussian distributions, and introduces generalized versions of Fisher information. The contributions of this paper are (i) the derivation of new extended Cramér-Rao inequalities for the estimation of a parameter, involving general q-moment...

On multidimensional generalized Cramér-Rao inequalities, uncertainty relations and characterizations of generalized q-Gaussian distributions

In the present work, we show how the generalized Cramér-Rao inequality for the estimation of a parameter, presented in a recent paper, can be extended to the mutidimensional case with general norms on Rn, and to a wider context. As a particular case, we obtain a new multidimensional Cramér-Rao inequality which is saturated by generalized q-Gaussian distributions. We also give another related Cr...

Some properties of generalized Fisher information in the context of nonextensive thermostatistics

We present two extended forms of Fisher information that fit well in the context of nonextensive thermostatistics. We show that there exists an interplay between these generalized Fisher information, the generalized q-Gaussian distributions and the q-entropies. The minimum of the generalized Fisher information among distributions with a fixed moment, or with a fixed qentropy is attained, in bot...