  One hundred seven ultraluminous X-ray (ULX) sources with 0.3-10.0 keV
luminosities in excess of 1e39 erg/s are identified in a complete sample of 127
nearby galaxies. The sample includes all galaxies within 14.5 Mpc above the
completeness limits of both the Uppsala Galaxy Catalog and the Infrared
Astronomical Satellite survey. The galaxy sample spans all Hubble types, a four
decade range in mass and in star-formation rate. ULXs are detected in this
sample at rates of one per 3.2e10 solar mass, one per 0.5 solar mass/year
star-formation rate, and one per 57 cubic Mpc corresponding to a luminosity
density of ~2e37 erg/s/Mpc3. At these rates we estimate as many as 19
additional ULXs remain undetected in fainter dwarf galaxies within the survey
volume. An estimated 14 or 13%, of the 107 ULX candidates are expected to be
background sources. The differential ULX luminosity function shows a power law
slope of -1.2 to -2.0 with an exponential cutoff at 2e40 erg/s with precise
values depending on the model and on whether the ULX luminosities are estimated
from their observed numbers of counts or, for a subset of candidates, from
their spectral shapes. Extrapolating the observed luminosity function predicts
at most one very luminous ULX, L~1e41 erg/s, within a distance as small as 100
Mpc. The luminosity distribution of ULXs within the local universe cannot
account for the recent claims of luminosities in excess of 2e41 erg/s requiring
a new population class to explain these extreme objects.
