The q-exponential family in statistical physics

The q-exponential family in statistical physics

The notion of generalised exponential family is considered in the restricted context of nonextensive statistical physics. Examples are given of models belonging to this family. In particular, the q-Gaussians are discussed and it is shown that the configurational probability distributions of the microcanonical ensemble belong to the q-exponential family.

Review of the Applications of Exponential Family in Statistical Inference

‎In this paper‎, ‎after introducing exponential family and a history of work done by researchers in the field of statistics‎, ‎some applications of this family in statistical inference especially in estimation problem‎,‎statistical hypothesis testing and statistical information theory concepts will be discussed‎.

Model Selection from the Q-exponential Family for Representing Statistical Shape Models of Organs

Exponential family models and statistical genetics.

This article describes the evolution of applied exponential family models, starting at 1972, the year of publication of the seminal papers on generalized linear models and on Cox regression, and leading to multivariate (i) marginal models and inference based on estimating equations and (ii) random effects models and Bayesian simulation-based posterior inference. By referring to recent work in g...

Estimators, Escort Probabilities, and Φ-exponential Families in Statistical Physics

The lower bound of Cramér and Rao is generalized to pairs of families of probability distributions, one of which is escort to the other. This bound is optimal for certain families, called φ-exponential in the paper. Their dual structure is explored. They satisfy a variational principle with respect to an appropriately chosen entropy functional, which is the dual of a free energy functional.