  The Hubble constant ($H_{0}$) is a measurement to describe the expansion rate
of the Universe in the current era. However, there is a $4.4\sigma$ discrepancy
between the measurements from the early Universe and the late Universe. In this
research, we propose a model-free and distance-free method to constrain
$H_{0}$. Combining Friedman-Lema\^itre-Robertson-Walker cosmology with
geometrical relation of the proper motion of extragalactic jets, the lower
limit ($H_{\rm 0,min}$) of $H_{0}$ can be determined using only three
cosmology-free observables: the redshifts of the host galaxies, as well as the
approaching and receding angular velocities of radio jets. Using these, we
propose to use the Kolmogorov-Smirnov test (K-S test) between cumulative
distribution functions of $H_{\rm 0,min}$ to differentiate cosmology. We
simulate 100, 200, and 500 extragalactic jets with 3 levels of accuracy of the
proper motion ($\mu_{a}$ and $\mu_{r}$), at $10\%$, $5\%$, and $1\%$,
corresponding to the accuracies of the current and future radio
interferometers. We perform K-S tests between the simulated samples as
theoretical distributions with different $H_{0}$ and power-law index of
velocity distribution of jets and mock observational data. Our result suggests
increasing sample sizes leads to tighter constraints on both power-law index
and the Hubble constant at moderate accuracy (i.e., $10\%$ and $5\%$) while at
$1\%$ accuracy, increasing sample sizes leads to tighter constraints on
power-law index more. Improving accuracy results in better constraints in the
Hubble constant compared with the power-law index in all cases but it
alleviates the degeneracy.
