Parameter estimation in non-extensive thermostatistics

Equilibrium statistical physics is considered from the point of view of statistical estimation theory. This involves the notions of statistical model, of estimators, and of exponential family. A useful property of the latter is the existence of identities, obtained by taking derivatives of the logarithm of the partition sum. It is shown that these identities still exist for models belonging to generalised exponential families, in which case they involve escort probability distributions. The percolation model serves as an example. A previously known identity is derived. It relates the average number of sites belonging to the finite cluster at the origin, the average number of perimeter sites, and the derivative of the order parameter.