# The luminosity function of quasars by the Principle of Maximum Entropy

## TL;DR

This paper introduces a novel application of the Principle of Maximum Entropy to derive the quasar luminosity function from SDSS-DR3 data, providing consistent estimates across various samples and redshifts.

## Contribution

It presents a new method using maximum entropy to estimate the quasar luminosity function from observational data, extending analysis to higher redshifts.

## Key findings

- Luminosity function estimates agree with previous studies.
- Results are robust to sample variations.
- Method effectively estimates luminosity distribution at high redshifts.

## Abstract

We propose a different way to obtain the distribution of the luminosity function of quasars by using the Principle of Maximum Entropy. The input data comes from the SDSS-DR3 quasars counts, extending up to redshift 5 and limited from apparent magnitude $i=15$ to 19.1 at $z\lesssim3$ to $i=20.2$ for $z\gtrsim3$. Using only few initial data points, the Principle allows us to estimate probabilities and hence that luminosity curve. We carry out statistical tests to evaluate our results. The resulting luminosity function compares well to earlier determinations. And our results remain consistent either when the amount or choice of sampled sources is unbiasedly altered. Besides this we estimate the distribution of the luminosity function for redshifts in which there is only observational data in the vicinity.