New probability distributions in astrophysics: I. The truncated generalized gamma

TL;DR

This paper introduces a new truncated generalized gamma distribution to model astrophysical luminosity functions, providing a more rigorous statistical tool for analyzing galaxy and quasar brightness across various surveys and redshift ranges.

Contribution

The paper develops and applies a novel truncated generalized gamma distribution with scale to astrophysical luminosity functions, improving modeling accuracy over traditional gamma functions.

Findings

The new truncated GG distribution fits luminosity data from SDSS, 2dF, and COSMOS surveys.

It models the magnitude-redshift relationship effectively.

Provides a flexible statistical framework for astrophysical luminosity analysis.

Abstract

The gamma function is a good approximation to the luminosity function of astrophysical objects, and a truncated gamma distribution would permit a more rigorous analysis. This paper examines the generalized gamma distribution (GG) and then introduces the scale and the new double truncation. The magnitude version of the truncated GG distribution with scale is adopted in order to fit the luminosity function (LF) for galaxies or quasars. The new truncated GG LF is applied to the five bands of SDSS galaxies, to the 2dF QSO Redshift Survey in the range of redshifts between 0.3 and 0.5, and to the COSMOS QSOs in the range of redshifts between 3.7 and 4.7. The average absolute magnitude versus redshifts for SDSS galaxies and QSOs of 2dF was modeled adopting a redshift dependence for the lower and upper absolute magnitude of the new truncated GG LF.