  The incomplete nonextensive statistics in the canonical and microcanonical
ensembles is explored in the general case and in a particular case for the
ideal gas. By exact analytical results for the ideal gas it is shown that
taking the thermodynamic limit, with $z=q/(1-q)$ being an extensive variable of
state, the incomplete nonextensive statistics satisfies the requirements of
equilibrium thermodynamics. The thermodynamical potential of the statistical
ensemble is a homogeneous function of the first degree of the extensive
variables of state. In this case, the incomplete nonextensive statistics is
equivalent to the usual Tsallis statistics. If $z$ is an intensive variable of
state, i.e. the entropic index $q$ is a universal constant, the requirements of
the equilibrium thermodynamics are violated.
