TITLE:
New Probability Distributions in Astrophysics: VIII. The Truncated Weibull—Pareto Distribution
AUTHORS:
Lorenzo Zaninetti
KEYWORDS:
Stars: Normal, Galaxy Groups, Clusters, Superclusters, Large Scale Structure of the Universe, Cosmology
JOURNAL NAME:
International Journal of Astronomy and Astrophysics,
Vol.12 No.2,
June
10,
2022
ABSTRACT: We derive the truncated version of the Weibull—Pareto distribution, deriving the probability density function, the distribution function, the average value, the rth moment about the origin, the media, the random generation of values and the maximum likelihood estimator which allows deriving the three parameters. The astrophysical applications of the Weibull—Pareto distribution are the initial mass function for stars, the luminosity function for the galaxies of the Sloan Digital Sky Survey, the luminosity function for QSO and the photometric maximum of galaxies of the 2 MASS Redshift Survey.