  Radiatively generated, LO quark (u,d,s,c,b) and gluon densities in the real,
unpolarized photon, calculated in the CJK model being an improved realization
of the CJKL approach, have been recently presented. The results were obtained
through a global fit to the experimental F2^gamma data. In this paper we
present, obtained for the very first time in the photon case, an estimate of
the uncertainties of the CJK parton distributions due to the experimental
errors. The analysis is based on the Hessian method which was recently applied
in the proton parton structure analysis. Sets of test parametrizations are
given for the CJK model. They allow for calculation of its best fit parton
distributions along with F2^gamma and for computation of uncertainties of any
physical value depending on the real photon parton densities. We test the
applicability of the approach by comparing uncertainties of example
cross-sections calculated in the Hessian and Lagrange methods. Moreover, we
present a detailed analysis of the chi^2 of the CJK fit and its relation to the
data. We show that large chi^2/DOF of the fit is due to only a few of the
experimental measurements. By excluding them chi^2/DOF approx 1 can be
obtained.
