Exploring new ways of distance determination and its applications to derive the most fundamental relations in astronomy

In this thesis we develop a pipeline using a statistical method to derive the distance of samples of galaxies to measure the number density of galaxies as a function of luminosity (the galaxy luminosity function). This distribution is of high importance as it gives constraints to the underlying physical processes involved in the evolution of galaxies. With this technique we were able to achieve deeper measurements of the galaxy luminosity function than with conventional methods, showing the potential of this technique for the next generation of galaxy surveys.