\begin{document}$ M_{\rm{B}} $\end{document} from SNIa and linear size scaling factor l from QSOs on the CDDR test. The results demonstrate that these prior values introduce significant biases in the CDDR test. To avoid the biases, we propose a method independent of \begin{document}$ M_{\rm{B}} $\end{document} and l to test the CDDR, which treats the fiducial value of a new variable \begin{document}$ \kappa\equiv 10^{M_{\rm{B}} \over 5}\,l $\end{document} as a nuisance parameter and then marginalize its impact with a flat prior in the statistical analysis. The results show that the CDDR is consistent with the observational data, and QSOs can serve as a powerful tool for testing the CDDR independent of cosmological models."> Testing the cosmic distance duality relation using Type Ia supernovae and radio quasars through model-independent methods -
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