A quick estimation of luminosity function based on the luminosity-distance diagram

Abstract: Based on the luminosity-distance diagram, we propose a method to quickly estimate the luminosity function for any certain astrophysical objects. Giving the mean distance between any two objects at a given luminosity range, we can find the relation between the mean distance and the luminosity, and consequently can obtain the luminosity function. Not like the straightforward counting method, this method does not need a complete sample. The only requirement is that the object distributes uniformly in space. We apply this method to a simulated sample, and find it can produce the luminosity function properly. This method can also be used for energy function.