  We estimate the local number density of sources of ultra-high-energy cosmic
rays (UHECRs) based on the statistical features of their arrival direction
distribution. We calculate the arrival distributions of protons above $10^{19}$
eV taking into account their propagation process in the Galactic magnetic field
and a structured intergalactic magnetic field, and statistically compare those
with the observational result of the Pierre Auger Observatory. The anisotropy
in the arrival distribution at the highest energies enables us to estimate the
number density of UHECR sources as $\sim 10^{-4} {\rm Mpc}^{-3}$ assuming the
persistent activity of UHECR sources. We compare the estimated number density
of UHECR sources with the number densities of known astrophysical objects. This
estimated number density is consistent with the number density of
Fanaroff-Reily I galaxies. We also discuss the reproducability of the observed
{\it isotropy} in the arrival distribution above $10^{19}$ eV. We find that the
estimated source model cannot reproduce the observed isotropy. However, the
observed isotropy can be reproduced with the number density of
$10^{-2}$-$10^{-3} {\rm Mpc}^{-3}$. This fact indicates the existence of UHECR
sources with a maximum acceleration energy of $\sim 10^{19}$ eV whose number
density is an order of magnitude more than that injecting the highest energy
cosmic rays.
