Escort Husimi distributions, Fisher information and nonextensivity

Escort–Husimi distributions, Fisher information and nonextensivity

We evaluate generalized information measures constructed with Husimi distributions and connect them with the Wehrl entropy, on the one hand, and with thermal uncertainty relations, on the other one. The concept of escort distribution plays a central role in such a study. A new interpretation concerning the meaning of the nonextensivity index q is thereby provided. A physical lower bound for q i...

On escort distributions, q-gaussians and Fisher information

Escort distributions are a simple one parameter deformation of an original distribution p. In Tsallis extended thermostatistics, the escort-averages, defined with respect to an escort distribution, have revealed useful in order to obtain analytical results and variational equations, with in particular the equilibrium distributions obtained as maxima of Rényi-Tsallis entropy subject to constrain...

Husimi Distribution and the Fisher Information

Fisher Information in Weighted Distributions

Standard inference procedures assume a random sample from a population with density fθ(x) for estimating the parameter θ. However, there are many applications in which the available data are a biased sample instead. Fisher modeled biased sampling using a weight function w(x) ≥ 0, and constructed a weighted distribution with a density f θ (x) that is proportional to w(x)fθ(x). In this paper, we ...

Superstatistics, escort distributions, and applications

Superpositions of different statistics on different time or spatial scales (in short, superstatistics) can naturally lead to an effective description by nonextensive statistical mechanics. We first discuss the role of escort distributions within the superstatistical framework, and then briefly describe recent physical applications of this concept to turbulent and patttern forming systems.