**3.3. TF Parameters Obtained from VELMOD**

The mock catalogs also enable us to test
the accuracy of the TF parameters determined from the likelihood
maximization procedure. The comparison of input and output values is given
in Table 1. The results for the TF
slope and scatter are
consistent with the statement that VELMOD returns unbiased values of these
TF parameters for each of the two samples. The fact that the TF scatters
and _{v}
are unbiased means that VELMOD correctly measures the overall variance in
peculiar velocity predictions.

The TF zero points returned by VELMOD are systematically in error by 2-3
standard deviations. This can be traced to a bias in the
*IRAS*-predicted peculiar velocities; the mean value of the quantity
*f* in Section 3.2 over 20
realizations was
0.018 ± 0.007. This bias makes the *IRAS*-predicted distances
*d*_{IRAS}
*cz*
- *u*_{IRAS} too large by a factor of 1.018, or ~ 0.04 mag,
as in fact we see in Table 1.
Thus, VELMOD
determines the TF zero points in such a way as to compensate for a
small systematic error in the *IRAS* predictions. We expect such
an error to be present in the real data as well, but it will be
completely absorbed into the TF zero points, and our derived value
of _{I}
will be unaffected.