  We construct a three-dimensional and redshift-evolutionary X-ray and
ultraviolet ($L_X-L_{UV}$) luminosity relation for quasars from the powerful
statistic tool called copula, and find that the constructed $L_X-L_{UV}$
relation from copula is more viable than the standard one and the observations
favor the redshift-evolutionary relation more than $3\sigma$. The Akaike and
Bayes information criterions indicate that the quasar data support strongly the
three-dimensional $L_X-L_{UV}$ relation. Our results show that the quasars can
be regarded as a reliable indicator of the cosmic distance if the $L_X-L_{UV}$
relation from copula is used to calibrate quasar data.
