On the product of two gamma variates with argument 2: Application to the luminosity function for galaxies

A new luminosity function for galaxies can be built starting from the product of two random variables X and Y represented by a gamma variate with argument 2. The mean, the standard deviation and the distribution function of this new distribution are computed. This new probability density function is assumed to describe the mass distribution of galaxies. Through a non linear rule of conversion from mass to luminosity a second new luminosity function for galaxies is derived. The test of reliability of these two luminosity functions was made on the Sloan Digital Sky Survey (SDSS) in five different bands. The Schechter function gives a better fit with respect to the two new luminosity functions for galaxies here derived.