  We present a new method for fitting peculiar velocity models to complete flux
limited magnitude-redshifts catalogues, using the luminosity function of the
sources as a distance indicator.The method is characterised by its robustness.
In particular, no assumptions are made concerning the spatial distribution of
sources and their luminosity function. Moreover, selection effects in redshift
are allowed. Furthermore the inclusion of additional observables correlated
with the absolute magnitude -- such as for example rotation velocity
information as described by the Tully-Fisher relation -- is straightforward.
  As an illustration of the method, the predicted IRAS peculiar velocity model
characterised by the density parameter beta is tested on two samples. The
application of our method to the Tully-Fisher MarkIII MAT sample leads to a
value of beta=0.6 \pm 0.125, fully consistent with the results obtained
previously by the VELMOD and ITF methods on similar datasets. Unlike these
methods however, we make a very conservative use of the Tully-Fisher
information. Specifically, we require to assume neither the linearity of the
Tully-Fisher relation nor a gaussian distribution of its residuals. Moreover,
the robustness of the method implies that no Malmquist corrections are
required.
  A second application is carried out, using the fluxes of the IRAS 1.2 Jy
sample as the distance indicator. In this case the effective depth of the
volume in which the velocity model is compared to the data is almost twice the
effective depth of the MarkIII MAT sample. The results suggest that the
predicted IRAS velocity model, while successful in reproducing locally the
cosmic flow, fails to describe the kinematics on larger scales.
