Application of the Information Criterion to the Estimation of Galaxy Luminosity Function

Abstract. 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 (Efstathiou, Ellis, & Peterson, 1988), 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 (Sandage, Tamman, & Yahil, 1979) with stepwise LF.