  We present the first joint analysis of catalogs of radio galaxies and quasars
to determine if their sky distribution is consistent with the standard
$\Lambda$CDM model of cosmology. This model is based on the cosmological
principle, which asserts that the universe is statistically isotropic and
homogeneous on large scales, so the observed dipole anisotropy in the cosmic
microwave background (CMB) must be attributed to our local peculiar motion. We
test the null hypothesis that there is a dipole anisotropy in the sky
distribution of radio galaxies and quasars consistent with the motion inferred
from the CMB, as is expected for cosmologically distant sources. Our two
samples, constructed respectively from the NRAO VLA Sky Survey and the
Wide-field Infrared Survey Explorer, are systematically independent and have no
shared objects. Using a completely general statistic that accounts for
correlation between the found dipole amplitude and its directional offset from
the CMB dipole, the null hypothesis is independently rejected by the radio
galaxy and quasar samples with $p$-value of $8.9\times10^{-3}$ and
$1.2\times10^{-5}$, respectively, corresponding to $2.6\sigma$ and $4.4\sigma$
significance. The joint significance, using sample size-weighted $Z$-scores, is
$5.1\sigma$. We show that the radio galaxy and quasar dipoles are consistent
with each other and find no evidence for any frequency dependence of the
amplitude. The consistency of the two dipoles improves if we boost to the CMB
frame assuming its dipole to be fully kinematic, suggesting that cosmologically
distant radio galaxies and quasars may have an intrinsic anisotropy in this
frame.
