Astronomers can accurately measure the galaxy positions on the sky. Unfortunately, it is not possible to have the same accuracy for the radial distance of each object. Different distance estimators are used in astronomy (see, for example, Ref. 1 for a review). For the luminosity selection effects one has to use the luminosity distance D_{l}, for the angular selection effects the angular diameter distance D_{a}, and in order to describe spatial clustering the comoving distance r is used. All these distances can be derived from the cosmological redshift of the galaxy z_{cos}. Distances however depend on the adopted cosmological model and the value of its parameters. For nearby galaxies, the Hubble law states that cz_{cos} = H_{0}r where H_{0} is the present value of the Hubble parameter. Recent measurements [2] provide a value of H_{0} = 72±8 km s^{-1} Mpc^{-1}. As space is curved, for more distant galaxies the distance-redshift relation is not linear any more, and different distances differ. We illustrate this in Fig. 1, where the different cosmological distances are given for the presently popular 'concordance model'. The statistics describing spatial clustering obviously depend on the adopted distance definitions, and thus on the prior cosmological model. This should be kept in mind, as these statistics are frequently used to estimate the 'true' parameters of the cosmological model.
It is important to mention that the true cosmological redshift is not a measurable quantity since what we really are able to measure for each galaxy is a quantity z satisfying the relation cz = cz_{cos} + v_{pec} where v_{pec} is the line-of-sight peculiar velocity. Peculiar velocities create a distorted version of the galaxy distribution - namely the redshift space -, as opposed to the real space where galaxies lie at their real positions. Distortions are more severe within the high density regions where effects like the Fingers-of-God - elongated structures along the line-of-sight - are the most evident consequence [3]. In next sections we will discuss how this distortions affect the statistical clustering measures.