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 .