  The equipartition theorem states that inverse temperature equals the
log-derivative of the density of states. This relation can be generalized by
introducing a proportionality factor involving an increasing positive function
phi(x). It is shown that this assumption leads to an equilibrium distribution
of the Boltzmann-Gibbs form with the exponential function replaced by a
deformed exponential function. In this way one obtains a formalism of
generalized thermostatistics introduced previously by the author. It is shown
that Tsallis' thermostatistics, with a slight modification, is the most obvious
example of this formalism and corresponds with the choice phi(x)=x^q.
