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A generalization of Student’s t-distribution from the viewpoint of special functions

Koepf, Wolfram
Masjed-Jamei, Mohammad

Student’s t-distribution has found various applications in mathematical statistics. One of the main properties of the t-distribution is to converge to the normal distribution as the number of samples tends to infinity. In this paper, by using a Cauchy integral we introduce a generalization of the t-distribution function with four free parameters and show that it converges to the normal distribution again. We provide a comprehensive treatment of mathematical properties of this new distribution. Moreover, since the Fisher F-distribution has a close relationship with the t-distribution, we also introduce a generalization of the F-distribution and prove that it converges to the chi-square distribution as the number of samples tends to infinity. Finally some particular sub-cases of these distributions are considered.

Citation
In: Mathematische Schriften Kassel 05, 17 / (2005) , S. ; 
@article{urn:nbn:de:hebis:34-2006060612898,
  author    ={Koepf, Wolfram and Masjed-Jamei, Mohammad},
  title    ={A generalization of Student’s t-distribution from the viewpoint of special functions},
  keywords ={510 and t-Verteilung and Normalverteilung and Gammaverteilung},
  copyright  ={https://rightsstatements.org/page/InC/1.0/},
  language ={en},
  year   ={2005}
}