  The Saha equation provides the relation between two consecutive ionization
state populations, like the Maxwell-Boltzmann velocity distribution of the
atoms in a gas ensemble. Saha equation can also consider the partitions
functions for both states and its main application is in stellar astrophysics
population statistics. This paper presents two non-Gaussian thermostatistical
generalizations for the Saha equation: the first one towards the Tsallis
nonextensive $q$-entropy and the other one is based upon Kaniadakis
$\kappa$-statistics. Both thermostatistical formalisms are very successful when
used in several complex astrophysical statistical systems and we have
demonstrated here that they work also in Saha's ionization distribution. We
have obtained new chemical $q$-potentials and their respective graphical
regions with a well defined boundary that separated the two symmetric intervals
for the $q$-potentials. The asymptotic behavior of the $q$-potential was also
discussed. Besides the proton-electron, we have also investigated the complex
atoms and pair production ionization reactions.
