  A spheroidal anisotropic local momentum distribution is implemented in the
statistical model of hadron production. We show that this form leads to exactly
the same ratios of hadronic abundances as the equilibrium distributions, if the
temperature is identified with a characteristic transverse-momentum scale.
Moreover, to a very good approximation the transverse-momentum spectra of
hadrons are the same for isotropic and anisotropic systems, provided the size
of the system at freeze-out is appropriately adjusted. We further show that
this invariance may be used to improve the agreement between the model and
experimental HBT results.
