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• TITLE: New Probability Distributions in Astrophysics: XI. Left Truncation for the Topp-Leone Distribution

  AUTHORS: Lorenzo Zaninetti

  KEYWORDS: Stars: Normal, Stars: Luminosity Function, Mass Function Stars: Statistics

  JOURNAL NAME: International Journal of Astronomy and Astrophysics, Vol.13 No.3, August 31, 2023

  ABSTRACT: The Topp-Leone (T-L) distribution has aided the modeling of scientific data in many contexts. We demonstrate how it can be adapted to model astrophysical data. We analyse the left truncated version of the T-L distribution, deriving its probability density function (PDF), distribution function, average value, rth moment about the origin, median, the random generation of its values, and its maximum likelihood estimator, which allows us to derive the two unknown parameters. The T-L distribution, in its regular and truncated versions, is then applied to model the initial mass function for the stars. A comparison is made with specific clusters and between proposed functions for the IMF. The Topp-Leone distribution can provide an excellent fit in some cases.