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Pearson, K. (1902) V. on the Methematical Theory of Errors of Judgement, with Special Reference to the Personal Equation. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 198, 235-299.

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• TITLE: New Probability Distributions in Astrophysics: XIV. Truncation of the Modified Lognormal Distribution

  AUTHORS: Lorenzo Zaninetti

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

  JOURNAL NAME: International Journal of Astronomy and Astrophysics, Vol.15 No.1, February 6, 2025

  ABSTRACT: In order to introduce left and right truncated versions of the modified lognormal with a power-law distribution, we derive its probability density function, its distribution function, its average value, its second moment of the origin, its variance, how to randomly generate its values, the maximum likelihood and the nonlinear least squares estimators for its three unknown parameters. It is then applied to five clusters of stars, to the mass function for stars, and to one catalog for the masses of the galaxies.