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.
Highlights
The generalized gamma distribution (GG) was introduced by [1] and carefully analyzed by [2]
A significant role in astrophysics is played by the luminosity function (LF) for galaxies and we present some models, among others, the Schechter LF, see [6], a two-component Schechter—like
Truncated LF: The truncated LF for galaxies or QSO is derived both in the luminosity form, see Equation (46), and in the magnitude form, see Equation (49)
Summary
The generalized gamma distribution (GG) was introduced by [1] and carefully analyzed by [2]. LF, see [7], and the double Schechter LF with five parameters, see [8] Another approach starts from a given statistical distribution for which the probability density function (PDF) is known. The above line of research allows exploring the LF for galaxies in the framework of well studied PDFs. Some examples are represented by the mass-luminosity relationship, see [9], some models connected with the generalized gamma (GG) distribution, see [10] [11], the truncated beta LF, see [12], the lognormal LF, see [13], the truncated lognormal LF, see [14], and the Lindley LF, see [15].
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