TITLE:
New Probability Distributions in Astrophysics: V. The Truncated Weibull Distribution
AUTHORS:
Lorenzo Zaninetti
KEYWORDS:
Stars: Normal, Galaxy Groups, Clusters, and Superclusters, Large Scale Structure of the Universe, Cosmology
JOURNAL NAME:
International Journal of Astronomy and Astrophysics,
Vol.11 No.1,
March
26,
2021
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 rth 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 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.