  The search for a luminosity function for galaxies both alternative or
companion to a Schechter function is a key problem in the reduction of data
from catalogs of galaxies. Two luminosity functions for galaxies can be built
starting from two distributions of mass as given by the fragmentation. A first
overall distribution function is the Kiang function that represents a useful
description of the area and volume distribution of the Poisson Voronoi
diagrams. The second distribution, that covers the case of low mass galaxies,
is the truncated Pareto distribution : in this model we have a natural bound
due to the minimum mass/luminosity observed and an upper bound (function of the
considered environment) represented by the boundary with the observed
mass/luminosity overall behaviour. The mass distribution is then converted into
a luminosity distribution through a standard mass-luminosity relationship.
