  This paper completes the statistical modeling of the Hubble flow when a
Tully-Fisher type relation is used for estimating the absolute magnitude
$M\approx a\,p+b$ from a line width distance indicator $p$. Our investigation
is performed with the aim of providing us with a full understanding of
statistical biases due to selection effects in observation, regardless of
peculiar velocities of galaxies. We show that unbiased $H_{\circ}$-statistics
can be obtained by means of the maximum likelihood method as long as the
statistical model can be defined. We focus on the statistical models related to
the Direct, resp. Inverse, Tully-Fisher relation, when selection effects on
distance, resp. on $p$, are present. It turns out that the use of the Inverse
relation should be preferred, according to robustness criteria. The formal
results are ensured by simulations with samples which are randomly generated
according to usual characteristics.
