TITLE:
New Probability Distributions in Astrophysics: X. Truncation and Mass-Luminosity Relationship for the Frèchet Distribution
AUTHORS:
Lorenzo Zaninetti
KEYWORDS:
Stars: Normal, Stars: Luminosity Function, Mass Function Stars: Statistics
JOURNAL NAME:
International Journal of Astronomy and Astrophysics,
Vol.12 No.4,
December
23,
2022
ABSTRACT: The Frèchet distribution has aided the modelling of scientific data in many contexts. We demonstrate how it can be adapted to model astrophysical data. We analyze the truncated version of the Frèchet distribution deriving the probability density function (PDF), the distribution function, the average value, the rth moment about the origin, the median, the random generation of values and the maximum likelihood estimator, which allows us to derive the two unknown parameters. This first PDF in the regular and truncated version is then applied to model the mass of the stars. A canonical transformation from the mass to the luminosity allows us to derive a new PDF, which is derived in its regular and truncated version. Finally, we apply this new PDF model on the distribution in luminosity of NGC 2362.