  The quantum version of Olbert's kappa distribution applicable to fermions is
obtained. Its construction is straightforward but requires recognition of the
differences in the nature of states separated by Fermi momenta. Its complement,
the bosonic version of the kappa distribution is also given, as is the
procedure of how to construct a hypothetical kappa-anyon distribution. At very
low temperature the degenerate kappa Fermi distribution yields a kappa-modified
version of the ordinary degenerate Fermi energy and momentum. We provide the
Olbert-generalized expressions of the Olbert-Fermi partition function and
entropy which may serve determining all relevant statistical mechanical
quantities. Possible applications are envisaged to condensed matter physics,
possibly quantum plasmas, and dense astrophysical objects like the interior
state of terrestrial planets, neutron stars, magnetars where quantum effects
come into play, dominate the microscopic scale but may have macroscopic
consequences.
