  The Maxwell distribution is derived from the $F$-distribution in the limit
where one of the degrees of freedom of the $\chi^2$ variates tends to infinity.
The estimator of the temperature is consistent, and, hence coincides with the
temperature of the heat reservoir in the asymptotic limit; it is also unbiased
and efficient. Consequently, there is a contradiction between indentifying the
Lagrange multiplier in the variational formalism that Tsallis and co-workers
use to maximize his nonadditive entropy with respect to escort expectation
values in order to derive the Student $t$- and $r$-distributions and the
physical meaning of these variables. Only in the asymptotic limit when these
distributions become the $\chi^2$-distributions of MBG statistics can the
Lagrange multiplier be interpreted as the inverse temperature. Hence, there is
no generalization of the $\chi^2$-distributions that can be made which involves
interpreting the Lagrange multiplier as the inverse temperature. The frequency
interpretation of the fluctuating temperature is contrasted with the Bayesian
approach that treats a parameter to be estimated as a random variable which is
equipped with a probability distribution.
