New probability distributions in astrophysics: V. The truncated Weibull distribution
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 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.
Keywords
Cite
@article{arxiv.2103.16346,
title = {New probability distributions in astrophysics: V. The truncated Weibull distribution},
author = {Lorenzo Zaninetti},
journal= {arXiv preprint arXiv:2103.16346},
year = {2021}
}
Comments
13 pages and 8 figures. arXiv admin note: text overlap with arXiv:1906.00739