  To determine the exact shape of the luminosity function (LF) of galaxies is
one of the central problems in galactic astronomy and observational cosmology.
The most popular method to estimate the LF is maximum likelihood, which is
clearly understood with the concepts of the information theory. In the field of
information theory and statistical inference, great advance has been made by
the discovery of Akaike's Information Criterion (AIC). It enables us to perform
a direct comparison among different types of models with different numbers of
parameters, and provides us a common basis of the model adequacy. In this paper
we applied AIC to the determination of the shape of the LF. We first treated
the estimation using stepwise LF, and derived a formula to obtain the optimal
bin number. In addition, we studied the method to compare the goodness-of-fit
of the parametric form with stepwise LF.
