  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 ${\Gamma _{UV}}$, the goodness of fit for RLQs with
${\Gamma _{UV}}\le 1.6$ 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.
