  A first new luminosity functions of galaxies can be built starting from a
left truncated beta probability density function, which is characterized by
four parameters. In the astrophysical conversion, the number of parameters
increases by one, due to the addition of the overall density of galaxies. A
second new galaxy luminosity function is built starting from a left truncated
beta probability for the mass of galaxies once a simple nonlinear relationship
between mass and luminosity is assumed; in this case the number of parameters
is six because the overall density of galaxies and a parameter that regulates
mass and luminosity are added. The two new galaxy luminosity functions with
finite boundaries were tested on the Sloan Digital Sky Survey (SDSS) in five
different bands; the results produce a "better fit" than the Schechter
luminosity function in two of the five bands considered. A modified Schechter
luminosity function with four parameters has been also analyzed.
