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 b
oth 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.
