  Quantitative differences of Lagrange multipliers between standard Fermi-Dirac
statistics (FDS) and Ionization energy ($E_I$) based FDS (iFDS) are analyzed in
detail to obtain reasonably accurate interpretations without violating the
standard FDS. The resistivity and Hall-resistance models in 1D, 2D and 3D are
also derived to illustrate the transport phenomena in semiconducting
manganites. It is shown via calculation that the charge carriers in these
materials seem to be strongly correlated in term of electron-ion attraction or
simply, fermions in those materials are somewhat gapped due to Coulomb
attraction. This Coulomb attraction naturally captures the polaronic effect in
manganites. $E_I$ is found to be the only essential parameter that predicts
$\rho(T,doping,pressure,magnetic field)$ quite accurately. However, this model
as will be pointed out, is not suitable for metals with free-electrons and
strong electron-phonon scattering. It is to be noted that iFDS and
$\rho(T,doping,pressure,magnetic field)$ model are only valid in the
paramagnetic region of ferromagnetic manganites and other doped-semiconductors.
Recent X-ray photoemission spectroscopy (XPS) studies have indicated that there
exists a critical crossover from Mn(2+) to Mn(3+) depending upon Mn's
concentrations in (Ga(1-x)Mnx)As diluted magnetic semiconductors (DMS). Such
phenomenon occuring at certain critical concentration directly point towards
the applicability of $E_I$ based Fermi-liquid (iFLT). As such, iFDS is also
discussed with respect to DMS above Curie temperature.
