  We have applied the proposed variability -> luminosity indicator to ten
"X-Ray Flashes" (XRFs) observed by the Wide-Field Cameras on BeppoSAX for which
BATSE survey data exists. Our results suggest that the variability ->
luminosity indicator probably works for XRFs. Assuming this to be so, we find
that the luminosity and redshift distributions of XRFs are consistent with
those of long-duration gamma-ray bursts (GRBs), and therefore most XRFs are
probably not very high redshift GRBs. The fact that XRFs and GRBs have similar
luminosity and redshift distributions suggests that XRFs and long-duration GRBs
are produced by a similar mechanism.
