In a previous paper, we have demonstrated the importance to define a
statistical model describing the observed linear correlation between the
absolute magnitude M and the log line width distance indicator p of
galaxies (the Tully-Fisher relation). As long as the same statistical model is
used during the calibration step of the relation and the step of the
determination of the distances of galaxies, standard statistical methods such
as the maximum likelihood technic permits us to derive bias free estimators of
the distances of galaxies. However in practice, it is convenient to use a
different statistical model for calibrating the Tully-Fisher relation (because
of its robustness, the Inverse Tully-Fisher relation is prefered during this
step) and for determining the distances of galaxies (the Direct Tully-Fisher
relation is more accurate and robust in this case). Herein, we establish a
correspondence between the Inverse and the Direct Tully-Fisher approaches.
Assuming a gaussian luminosity function, we prove that the ITF and DTF models
are in fact mathematically equivalent (i.e. they describe the same physical
data distribution in the TF diagram). It thus turns out that as long as the
calibration parameters are obtained for a given model, we can deduce the
corresponding parameters of the other model. We present these formulae of
correspondence and discuss their validitity for non-gaussian luminosity
functions.Comment: 10 pages, uuencoded en compressed Postscript file, figures avaible
under requests. To be published in A\&
