New Probability Distributions in Astrophysics: V. The Truncated Weibull Distribution

• 作者: Lorenzo Zaninetti
• 来源期刊: 天文学与天体物理学国际期刊(英文)
• 学科: 地球科学
• 关键词: Stars: Normal Galaxy Groups CLUSTERS and Superclusters Large Scale Structure of the Universe COSMOLOGY
• 年，卷（期）: 2021,（1）
• 页码范围: 133-149
• 页数: 17页
• 分类号: P15

摘要

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 <em>r</em>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 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.