A B S T R A C TWe propose a test which allows us to check whether a luminosity function model can account for the intrinsic luminosity distribution of a magnitude -redshift sample complete in apparent magnitude. No a priori assumptions are required concerning the redshift-space distribution of the sources, so neither the clustering nor an eventual evolution of the mean number density of the galaxies affects the conclusions of the goodness-of-fit test. The statistical efficiency of the test, if used as a fitting technique for estimating the best-fitting solution of a parametric luminosity function model, is comparable to the efficiency of standard maximum likelihood fitting techniques. The goodness-of-fit test presents however a major improvement compared with fitting techniques in general: the capacity to assess the adequacy of the proposed parametric model to the data. The computational implementation of this new test is straightforward. Its potential is illustrated on the Southern Sky Redshift Survey of da Costa et al.

We present a brief overview and preliminary measure of the Local Group velocity, using the PSCz survey together with its recently completed extension into the Galactic plane, the Behind The Plane (BTP) survey. The addition of the BTP has increased the total sky coverage from 84% to 93%, drastically reducing the systematic uncertainty in the direction of the local gravitational pull caused by incomplete sky coverage. We present methods that self-consistently determine the acceleration in the presence of redshift distortions. Preliminary results suggest that the dipole converges within the survey limiting depth. There is a large, but only marginally significant, component to the dipole arising at 180-200 h −1 Mpc.Keywords: cosmology: large-scale structure -galaxies: kinematics and dynamics Behind The Plane Extension SurveyThe BTP is the low-latitude extension to the PSCz (Point Source Catalogue redshift) survey (Saunders et al. 2000a) based on the IRAS PSC, which mapped the entire sky at 12, 25, 60, and 100 µm, with nearly uniform all-sky coverage -ideal as an all-sky redshift catalogue sample base. The IRAS selection criteria were tightened for the BTP, in order to minimise contamination from Galactic sources. These criteria were S 60 > 2 S 25 and S 60 > 4 S 12 to exclude stars, and S 100 < 5 S 60 to exclude Galactic cirrus. Also excluded were areas with <2 HCONS, areas of high source density at 12, 25, and 60 µm, and areas with I 100 > 25 MJy sr −1 . The remaining unmapped sky is due to the IRAS coverage gaps (3%) and the ZOA (4%). The survey has a median depth of 8500 km s −1 with low and quantified incompleteness. The BTP consists of 1225 PSC likely or confirmed galaxies, of which 869 have positive IDs and redshifts. Completeness issues are briefly described in Saunders et al. (2000b), and will be covered in detail in the official survey release (Saunders et al., in prep.). Local Group VelocityHere we describe the problems created when using a magnitude-limited redshift sample to measure the Local Group velocity v LG . Linear gravitational instability theory states that the velocity vector can in principle, be determined by integrating the gravitational force from the density field over the entire volume of the Universe (Peebles 1980). In reality we can make an estimate of this, using a sparse sample of the density field over a sufficiently large, finite volume. By using luminous galaxies as a tracer of the underlying mass, we getHere, β = 0.6 /b, where b is the bias of the galaxy population under consideration, and ψ(r) is the selection function -the expected number density of galaxies (in the absence of clustering) meeting the survey selection criteria, as a function of position (Strauss et al. 1992). The issue being that we have a redshift-space sample, but want real-space distances to each galaxy. For many cosmological statistics, these redshift-space distortions are critical. Conversely, the Local Group velocity is only sensitive to first-order changes in the mass distribution: non-linear distor...