%0 Journal Article
%T New Probability Distributions in Astrophysics: XI. Left Truncation for the Topp-Leone Distribution
%A Lorenzo Zaninetti
%J International Journal of Astronomy and Astrophysics
%P 154-165
%@ 2161-4725
%D 2023
%I Scientific Research Publishing
%R 10.4236/ijaa.2023.133009
%X 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, <em>r</em>th 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.
%K Stars: Normal
%K Stars: Luminosity Function
%K Mass Function Stars: Statistics
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=127397