天体物理学中的新概率分布：V.截尾威布尔分布
New probability distributions in astrophysics: V. The truncated Weibull distribution
摘要：
我们证明，某些天体物理分布可以建模与截断威布尔分布，这可以导致一些见解：特别是，我们报告的平均值，$r$ th时刻，方差，中位数，模式，随机数的生成，和评估的两个参数与极大似然估计。威布尔分布的第一个应用是恒星的初始质量函数。威布尔分布的星等版本被应用到斯隆数字巡天（SDSS）星系的光度函数和2MASS红移巡天（2MRS）星系的光度最大值。截断威布尔光度函数允许我们建模的绝对星等的平均值作为红移的2MRS星系的函数。
英文摘要：
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 $r$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.
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