  We consider the extension of the statistical parton distributions to include
their transverse momentum dependence, by using two different methods, one is
based on our quantum statistical approach, the other on a relativistic
covariant method. We take into account the effects of the Melosh-Wigner
rotation for the polarized distributions. The results obtained can be compared
with recent semiinclusive Deep Inelastic Scattering data on the cross section
and double longitudinal-spin asymmetries from JLab. We also give some
predictions for future experiments on electron-neutron scattering.
