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

作　　者：Lorenzo Zaninetti Lorenzo Zaninetti(Physics Department, University of Turin, Turin, Italy)

机构地区：[1]Physics Department, University of Turin, Turin, Italy

出　　处：《International Journal of Astronomy and Astrophysics》2023年第3期154-165,共12页天文学与天体物理学国际期刊（英文）

摘　　要：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.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.

关 键 词：Stars: Normal Stars: Luminosity Function Mass Function Stars: Statistics 

分 类 号：O17[理学—数学]