  The gamma function is a good approximation to the luminosity function of
astrophysical objects, and a truncated gamma distribution would permit a more
rigorous analysis. This paper examines the generalized gamma distribution (GG)
and then introduces the scale and the new double truncation. The magnitude
version of the truncated GG distribution with scale is adopted in order to fit
the luminosity function (LF) for galaxies or quasars. The new truncated GG LF
is applied to the five bands of SDSS galaxies, to the 2dF QSO Redshift Survey
in the range of redshifts between 0.3 and 0.5, and to the COSMOS QSOs in the
range of redshifts between 3.7 and 4.7. The average absolute magnitude versus
redshifts for SDSS galaxies and QSOs of 2dF was modeled adopting a redshift
dependence for the lower and upper absolute magnitude of the new truncated GG
LF.
