  We present a statistical analysis of the properties of galaxies containing
ultraluminous X-ray objects (ULXs). Our primary goal is to establish the
fraction of galaxies containing a ULX as a function of ULX luminosity. Our
sample is based on ROSAT HRI observations of galaxies. We find that ~ 12% of
galaxies contain at least one ULX with L_X > 10^39 erg/s and ~ 1% of galaxies
contain at least one ULX with L_X > 10^40 erg/s. These ULX frequencies are
lower limits since ROSAT HRI observation would miss absorbed ULXs (i.e., with
N_H >~ 10^21 cm^-2) and those within ~ 10" of the nucleus (due to the
positional error circle of the ROSAT HRI). The Hubble type distribution of
galaxies with a ULX differs significantly from the distribution of types for
nearby RC3 galaxies, but does not differ significantly from the galaxy type
distribution of galaxies observed by the HRI in general. We find no increase in
the mean FIR luminosity or FIR / K band luminosity ratio for galaxies with a
ULX relative to galaxies observed by the HRI in general, however this result is
also most likely biased by the soft bandpass of the HRI and the relatively low
number of high SFR galaxies observed by the HRI with enough sensitivity to
detect a ULX.
