  Radiatively generated, LO quark (u,d,s,c,b) and gluon densities in the real,
unpolarized photon, improved in respect to our previous paper, are presented.
We perform three global fits to the F_2^gamma data, using the LO DGLAP
evolution equation. We improve the treatment of the strong coupling running and
used lower values of Lambda_QCD, as we have found that the too high values
adopted in the previous work caused the high chi^2 of the fits. In addition to
the modified FFNS_CJKL model, referred to as FFNS_CJK 1 we analyse a FFNS_CJK 2
model in which we take into account the resolved-photon heavy-quark
contribution. New CJK model with an improved high-x behavior of the
F_2^gamma(x,Q^2) is proposed. Finally, in the case of the CJK model we abandon
the valence sum rule imposed on the VMD input densities. New fits give chi^2
per degree of freedom about 0.25 better than the old results. All features of
the CJKL model, such as the realistic heavy-quark distributions, good
description of the LEP data on the Q^2 dependence of the F_2^gamma and on
F_2,c^gamma are preserved. Moreover we present results of an analysis of the
uncertainties of the CJK parton distributions due to the experimental errors.
It is based on the Hessian method used for the proton and very recently applied
for the photon by one of us. Parton and structure function parametrizations of
the best fits in both FFNS_CJK and CJK approaches are made accessible. For the
CJK model we provide also sets of test parametrizations which allow for
calculation of uncertainties of any physical value depending on the real photon
parton densities.
