Journal article
A generalization of Student's t-distribution from the viewpoint of special functions



Publication Details
Authors:
Koepf, W.; Masjed-Jamei, M.
Publication year:
2006
Journal:
Integral Transforms and Special Functions
Pages range:
863-875
Volume number:
17
Start page:
863
End page:
875
ISSN:
1065-2469

Abstract
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.


Research Areas


Last updated on 2019-01-11 at 16:05