  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.
