It is characterized by using the superposition of multiple differing statistical models to achieve the desired non-linearity.
In terms of ordinary statistical ideas, this is equivalent to compounding the distributions of random variables and it may be considered a simple case of a doubly stochastic model.
Consider[3] an extended thermodynamical system which is locally in equilibrium and has a Boltzmann distribution, that is the probability of finding the system in a state with energy
A non-equilibrium thermodynamical system is modeled by considering macroscopic fluctuations of the local inverse temperature.
, the superstatistical Boltzmann factor of the system is given by This defines the superstatistical partition function for system that can assume discrete energy states
follows a Gamma distribution, the resulting superstatistics corresponds to Tsallis statistics.
[4] Superstatistics can also lead to other statistics such as power-law distributions or stretched exponentials.
[5][6] One needs to note here that the word super here is short for superposition of the statistics.
This branch is highly related to the exponential family and Mixing.