We obtain a new sample of 1192 Type I quasars with the UV-optical, radio and X-ray wavebands coverage by combining \citet{Huang2022} and other matching data of SDSS-DR16 with FIRST, XMM-Newton, and Chandra Source Catalog, and a sample of 407 flat-spectrum radio-loud quasars (FSRLQs) of blazars from the Roma-BZCAT, which can be used to investigate their multi-band luminosity correlations and measure the luminosity distances of these Type I radio-loud quasars (RLQs) samples. We check the correlation between X-ray, UV-optical, and radio luminosity for various groupings of radio-quiet quasars (RQQs) and RLQs by parameterizing X-ray luminosity as a sole function of UV-optical or radio luminosity and as a joint function of UV-optical radio luminosity, which also can be employed to determine these cosmological distances. By Bayesian information criterion (BIC), the data suggest that the X-ray luminosity of RQQs is indirectly correlative with radio luminosity because of the connection between UV-optical and radio luminosity. But for RLQs, the X-Ray luminosity is directly related to radio luminosity, and the correlations between X-ray, optical/UV, and radio luminosity increase with the ratio of monochromatic luminosities logR. Meanwhile, we compare the results from RLQs with different UV-optical power law index ${Γ_{UV}}$, the goodness of fit for RLQs with ${Γ_{UV}}\le 1.6$ seems to be better. Finally, we apply a combination of Type I RLQs and SN Ia Pantheon to verify the nature of dark energy concerning whether or not its density deviates from the constant, and give the statistical results.

arXiv admin note: text overlap with arXiv:2207.08390