New probability distributions in astrophysics: V. The truncated Weibull distribution

TL;DR

This paper introduces the truncated Weibull distribution as a versatile model for astrophysical data, providing methods to estimate its parameters and applying it to stellar initial mass functions and galaxy luminosity functions.

Contribution

It presents the first application of the truncated Weibull distribution to astrophysical distributions, including parameter estimation and modeling of galaxy luminosity functions.

Findings

The distribution can model stellar initial mass functions.

It effectively fits galaxy luminosity functions from SDSS and 2MRS.

Provides analytical expressions for moments and median.

Abstract

We demonstrate that certain astrophysical distributions can be modelled with the truncated Weibull distribution, which can lead to some insights: in particular, we report the average value, the $r$th moment, the variance, the median, the mode, the generation of random numbers, and the evaluation of the two parameters with maximum likelihood estimators. The first application of the Weibull distribution is to the initial mass function for stars. The magnitude version of the Weibull distribution is applied to the luminosity function for the Sloan Digital Sky Survey (SDSS) galaxies and to the photometric maximum of the 2MASS Redshift Survey (2MRS) galaxies. The truncated Weibull luminosity function allows us to model the average value of the absolute magnitude as a function of the redshift for the 2MRS galaxies.