Observations favor the redshift-evolutionary $L_X$-$L_{UV}$ relation of quasars from copula

We compare, with data from the quasars, the Hubble parameter measurements, and the Pantheon+ type Ia supernova, three different relations between X-ray luminosity ($L_X$) and ultraviolet luminosity ($L_{UV}$) of quasars. These three relations consist of the standard and two redshift-evolutionary $L_X$-$L_{UV}$ relations which are constructed respectively by considering a redshift dependent correction to the luminosities of quasars and using the statistical tool called copula. By employing the PAge approximation for a cosmological-model-independent description of the cosmic background evolution and dividing the quasar data into the low-redshift and high-redshift parts, we find that the constraints on the PAge parameters from the low-redshift and high-redshift data, which are obtained with the redshift-evolutionary relations, are consistent with each other, while they are not when the standard relation is considered. If the data are used to constrain the coefficients of the relations and the PAge parameters simultaneously, then the observations support the redshift-evolutionary relations at more than $3\sigma$. The Akaike and Bayes information criteria indicate that there is strong evidence against the standard relation and mild evidence against the redshift-evolutionary relation constructed by considering a redshift dependent correction to the luminosities of quasars. This suggests that the redshift-evolutionary $L_X$-$L_{UV}$ relation of quasars constructed from copula is favored by the observations.