Application of the information criterion to the estimation of galaxy luminosity function

To determine the exact shape of the luminosity function (LF) of galaxies is one of the central problems in galactic astronomy and observational cosmol ogy. The most popular method to estimate the LF is maximum likelihood, whic h is clearly understood with the concepts of the information theory. In the field of information theory and statistical inference, great advance has b een made by the discovery of Akaike's Information Criterion (AIC). It enabl es us to perform a direct comparison among different types of models with d ifferent 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 o f the LF. We first treated the estimation using stepwise LF(Efstathiou, Ell is and Peterson, 1988), and derived a formula to obtain the optimal bin num ber. In addition, we studied the method to compare the goodness-of-fit of t he parametric form (Sandage, Tamman and Yahil, 1979) with stepwise LF.