  We compare two approaches to the generalization of the ordinary
Fermi-statistics based on the nonadditive Tsallis $q$-exponential used in the
Gibbs factor instead of the conventional exponential function. Both numerical
and analytical calculations are made for the chemical potential, fugacity,
energy, and the specific heat of the ideal gas obeying such generalized types
of statistics. In the approach based on the Gibbs factor containing the
chemical potential, high temperature behavior of the specific heat
significantly deviates from the expected classical limit, while at low
temperatures it resembles that of the ordinary ideal Fermi-gas. On the
contrary, when the fugacity enters as a multiplier at the Gibbs factor, the
high-temperature limit reproduces the classical ideal gas correctly. At low
temperatures, however, some interesting results are observed, corresponding to
non-zero specific heat at the absolute zero temperature or a finite (non-zero)
minimal temperature. These results, though exotic from the first glance, might
be applicable in effective modeling of physical phenomena in various domains.
