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Gompertz, B. (1825) On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies. In a Letter to Francis Baily, Esq. F.R.S. &c. Philosophical Transactions of the Royal Society of London, 115, 513-583.
https://doi.org/10.1098/rstl.1825.0026

has been cited by the following article:

• TITLE: New Probability Distributions in Astrophysics: XII. Truncation for the Gompertz Distribution

  AUTHORS: Lorenzo Zaninetti

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

  JOURNAL NAME: International Journal of Astronomy and Astrophysics, Vol.14 No.2, June 17, 2024

  ABSTRACT: Analytical functions which fit the probability distributions of stars and galaxies can provide insight into how these distributions originate. In order to introduce a truncated version of the Gompertz distribution, we derive its probability density function, its distribution function, its average value, its second moment about the origin, its median, its random generation of values and a maximum likelihood estimator for its two unknown parameters. The astrophysical applications of the Gompertz distribution are the initial mass function for stars, the luminosity function for the galaxies of the Sloan Digital Sky Survey, the photometric maximum of galaxies visible in the GLADE+ catalog and a model for the mean absolute magnitude in the GLADE+ catalog as a function of the redshift.